7. Systems of Equations & Matrices

Introduction to Matrices

7. Systems of Equations & Matrices

Introduction to Matrices

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Introduction to Matrices

Performing Row Operations on Matrices

Solving Systems of Equations - Matrices (Row-Echelon Form)

Solving Systems of Equations - Matrices (Reduced Row-Echelon Form)

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Gaussian Elimination with Back Substitution

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Gaussian Elimination with Back Substitution

Mario's Math Tutoring

Solve linear systems using Gaussian elimination with back substitution

Gaussian Elimination & Row Echelon Form

The Organic Chemistry Tutor

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❤︎² Gaussian Elimination.. How? (mathbff)

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❤︎² Gaussian Elimination.. How? (mathbff)

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Practice this topic

Multiple Choice

Write the equations in standard form, then represent the system using an augmented matrix.

$3x+5y-9=0$

$8x=-4y+3$

Perform the indicated Row Operation.

SWAP $R_1\leftrightarrow R_2$

Perform the indicated Row Operation.

ADD $R_1+2\cdot R_3\rightarrow R_1$

Solve the system of equations by using row operations to write a matrix in REDUCED row-echelon form.

$4x+2y+3z=6$

$x+y+z=3$

$5x+y+2z=5$

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Multiple Choice

Write the system of equations represented by the augmented matrix shown.

In Exercises 1–8, write the augmented matrix for each system of linear equations.

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Textbook Question

In Exercises 1–2, perform each matrix row operation and write the new matrix.

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Textbook Question

How many rows and how many columns does this matrix have? What is its dimension? <4x2 Matrix>

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Textbook Question

In Exercises 1 - 4, a. Give the order of each matrix, b. If A = [a_ij], identify a_32 and a_23, or explain why identification is not possible, 4 - 7 5 - 6 8 - 1 (please enclose the values above in a matrix symbol)

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Textbook Question

In Exercises 1–8, write the augmented matrix for each system of linear equations.

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Textbook Question

In Exercises 3–5, solve each system of equations using matrices. Use Gaussian elimination with back-substitution or Gauss-Jordan elimination.

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Textbook Question

What is the augmented matrix of the following system? -3x + 5y = 2 6x + 2y = 7

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Textbook Question

In Exercises 3–5, solve each system of equations using matrices. Use Gaussian elimination with back-substitution or Gauss-Jordan elimination.

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Textbook Question

In Exercises 3–5, solve each system of equations using matrices. Use Gaussian elimination with back-substitution or Gauss-Jordan elimination.

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Textbook Question

In Exercises 1–8, write the augmented matrix for each system of linear equations.

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Textbook Question

Use the given row transformation to change each matrix as indicated. See Sample 1. < 2x2 Matrix > ; -4 times row 1 added to row 2

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Textbook Question

In Exercises 1–8, write the augmented matrix for each system of linear equations.

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Textbook Question

Use the given row transformation to change each matrix as indicated. See Sample 1. < 2x2 Matrix > ; -7 times row 1 added to row 2

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Textbook Question

In Exercises 9-12, write the system of linear equations represented by the augmented matrix. Use x, y, and z, or, if necessary, w, x, y, and z, for the variables.

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Textbook Question

Use the given row transformation to change each matrix as indicated. See Sample 1. < 3x3 Matrix > ; 2 times row 1 added to row 2

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Textbook Question

In Exercises 9 - 16, find the following matrices: b. A - B 4 1 5 9 A = B = 3 2 0 7

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Textbook Question

Find the dimension of each matrix. Identify any square, column, or row matrices. See the discussion preceding Example 1.

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Textbook Question

In Exercises 9 - 16, find the following matrices: d. - 3A + 2B 4 1 5 9 A = B = 3 2 0 7

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Textbook Question

Use the given row transformation to change each matrix as indicated. See Sample 1. < 3x3 Matrix > ; 4 times row 1 added to row 2

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Textbook Question

In Exercises 9-12, write the system of linear equations represented by the augmented matrix. Use x, y, and z, or, if necessary, w, x, y, and z, for the variables.

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Textbook Question

In Exercises 9 - 16, find the following matrices: a. A + B 3 1 1 2 - 3 6 A = B = - 1 2 5 - 3 1 - 4

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Textbook Question

In Exercises 9 - 16, find the following matrices: d. - 3A + 2B 3 1 1 2 - 3 6 A = B = - 1 2 5 - 3 1 - 4

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Textbook Question

In Exercises 9 - 16, find the following matrices: c. - 4A 3 1 1 2 - 3 6 A = B = - 1 2 5 - 3 1 - 4

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Textbook Question

Write the augmented matrix for each system and give its dimension. Do not solve. 2x + y + z - 3 = 0 3x - 4y + 2z + 7 = 0 x + y + z - 2 = 0

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Textbook Question

In Exercises 13–18, perform each matrix row operation and write the new matrix.

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Textbook Question

Write the augmented matrix for each system and give its dimension. Do not solve. 4x - 2y + 3z - 4 = 0 3x + 5y + z - 7 = 0 5x - y + 4z - 7 = 0

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Textbook Question

In Exercises 14–27, perform the indicated matrix operations given that and D are defined as follows. If an operation is not defined, state the reason. A+D

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Textbook Question

In Exercises 9 - 16, find the following matrices: a. A + B A = [6 2 - 3], B = [4 - 2 3]

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Textbook Question

In Exercises 9 - 16, find the following matrices: c. - 4A A = [6 2 - 3], B = [4 - 2 3]

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Textbook Question

In Exercises 13–18, perform each matrix row operation and write the new matrix.

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Textbook Question

Write the system of equations associated with each augmented matrix . Do not solve. <4x3 Matrix>

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Textbook Question

In Exercises 9 - 16, find the following matrices: d. - 3A + 2B 2 - 10 - 2 6 10 - 2 A = 14 12 10 B = 0 - 12 - 4 4 - 2 2 - 5 2 - 2

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Textbook Question

In Exercises 14–27, perform the indicated matrix operations given that and D are defined as follows. If an operation is not defined, state the reason. D-A

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Textbook Question

In Exercises 13–18, perform each matrix row operation and write the new matrix.

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Textbook Question

Write the system of equations associated with each augmented matrix . Do not solve. <4x3 Matrix>

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Textbook Question

In Exercises 14–27, perform the indicated matrix operations given that and D are defined as follows. If an operation is not defined, state the reason. 3A+2D

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Textbook Question

In Exercises 19–20, a few steps in the process of simplifying the given matrix to row-echelon form, with 1s down the diagonal from upper left to lower right, and 0s below the 1s, are shown. Fill in the missing numbers in the steps that are shown.

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Textbook Question

Write the system of equations associated with each augmented matrix . Do not solve.

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Textbook Question

Find the values of the variables for which each statement is true, if possible. See Examples 1 and 2. =

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Textbook Question

In Exercises 17 - 26, let - 3 - 7 - 5 - 1 A = 2 - 9 and B = 0 0 5 0 3 - 4 Solve each matrix equation for X. 2X + A = B

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Textbook Question

In Exercises 14–27, perform the indicated matrix operations given that and D are defined as follows. If an operation is not defined, state the reason. -5(A+D)

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Textbook Question

Use the Gauss-Jordan method to solve each system of equations. For systems in two variables with infinitely many solutions, write the solution with y arbitrary. For systems in three variables with infinitely many solutions, write the solution set with z arbitrary. See Examples 1-4. x + y = 5 x - y = -1

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Textbook Question

In Exercises 21–38, solve each system of equations using matrices. Use Gaussian elimination with back-substitution or Gauss-Jordan elimination.

In Exercises 21–38, solve each system of equations using matrices. Use Gaussian elimination with back-substitution or Gauss-Jordan elimination.

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Textbook Question

In Exercises 14–27, perform the indicated matrix operations given that and D are defined as follows. If an operation is not defined, state the reason. BD

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Textbook Question

Solve each system, using the method indicated. 5x + 2y = -10 3x - 5y = -6 (Gauss-Jordan)

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Textbook Question

In Exercises 21–38, solve each system of equations using matrices. Use Gaussian elimination with back-substitution or Gauss-Jordan elimination.

In Exercises 21–38, solve each system of equations using matrices. Use Gaussian elimination with back-substitution or Gauss-Jordan elimination.

Solve each system, using the method indicated. 3x + y = -7 x - y = -5 (Gaussian elimination)

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Textbook Question

Solve for X in the matrix equation 3X+A = B where

Solve each system, using the method indicated. x - z = -3 y + z = 6 2x - 3z = -9 (Gauss-Jordan)

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Textbook Question

In Exercises 21–38, solve each system of equations using matrices. Use Gaussian elimination with back-substitution or Gauss-Jordan elimination.

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Textbook Question

In Exercises 27 - 36, find (if possible) the following matrices: a. AB b. BA 1 2 A = [1 2 3 4], B = 3 4

In Exercises 21–38, solve each system of equations using matrices. Use Gaussian elimination with back-substitution or Gauss-Jordan elimination.

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Textbook Question

In Exercises 21–38, solve each system of equations using matrices. Use Gaussian elimination with back-substitution or Gauss-Jordan elimination.

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Textbook Question

In Exercises 27 - 36, find (if possible) the following matrices: a. AB b. BA 4 2 2 3 4 A = 6 1 B = 3 5 - 1 - 2 0

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Textbook Question

In Exercises 21–38, solve each system of equations using matrices. Use Gaussian elimination with back-substitution or Gauss-Jordan elimination.

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Textbook Question

In Exercises 21–38, solve each system of equations using matrices. Use Gaussian elimination with back-substitution or Gauss-Jordan elimination.

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Textbook Question

Find the quadratic function f(x) = ax² + bx + c for which ƒ( − 2) = −4, ƒ(1) = 2, and f(2) = 0.

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Textbook Question

Find each sum or difference, if possible. See Examples 2 and 3. <1x4 Matrix> - <1x4 Matrix>

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Textbook Question

Find the cubic function f(x) = ax³ + bx² + cx + d for which ƒ( − 1) = 0, ƒ(1) = 2, ƒ(2) = 3, and ƒ(3) = 12.

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Textbook Question

Solve the system: (Hint: Let A = ln w, B = ln x, C = ln y, and D = ln z. Solve the system for A, B, C, and D. Then use the logarithmic equations to find w, x, y, and z.)

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Textbook Question

In Exercises 37 - 44, perform the indicated matrix operations given that A, B and C are defined as follows. If an operation is not defined, state the reason. 4 0 5 1 1 - 1 A = - 3 5 B = C = 0 1 - 2 - 2 - 1 1 A(BC)

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Textbook Question

Let A = and B = . Find each of the following. See Examples 2 –4. (3/2)B

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Textbook Question

Find each product, if possible. See Examples 5–7. <4x2 Matrix>

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Textbook Question

Find the values of the variables for which each statement is true, if possible. [2x2 matrix] = [2x2 matrix]

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Textbook Question

Solve by eliminating variables:

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Textbook Question

Solve each system in Exercises 25–26. (x+3)/2 − (y−1)/2 + (z+2)/4 = 3/2, (x−5)/2 + (y+1)/3 − z/4 = − 25/6, (x−3)/4 − (y+1)/2 + (z−3)/2= − 5/2

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Textbook Question

Solve each system in Exercises 25–26. (x+2)/6 − (y+4)/3 + z/2 = 0, (x+1)/2 + (y−1)/2 − z/4 = 9/2, (x−5)/4 + (y+1)/3 + (z−2)/2 = 19/4

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Textbook Question

Exercises 57–59 will help you prepare for the material covered in the next section. Solve: A + B = 3, 2A - 2B + C = 17, 4A - 2C =14

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Textbook Question

In Exercises 19–22, find the quadratic function y = ax^2+bx+c whose graph passes through the given points. (−1,−4), (1,−2), (2, 5)

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In Exercises 19–22, find the quadratic function y = ax^2+bx+c whose graph passes through the given points. (−1, 6), (1, 4), (2, 9)

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Textbook Question

Solve each system in Exercises 5–18. 3(2x+y)+5z=−1, 2(x−3y+4z)=−9, 4(1+x)=−3(z−3y)

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Solve each system in Exercises 5–18. x+y=−4, y−z=1, 2x+y+3z=−21

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Solve each system in Exercises 5–18. 2x+y=2, x+y−z=4, 3x+2y+z=0

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Textbook Question

Solve each system in Exercises 5–18. 2x−4y+3z=17, x+2y−z=0, 4x−y−z=6

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Solve each system in Exercises 5–18. 3x+2y−3z=−2, 2x−5y+2z=−2, 4x−3y+4z= 10

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Textbook Question

Solve each system in Exercises 5–18. 4x−0y+2z=11, x+2y−z=−1, 2x+2y−3z=−1

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Solve each system in Exercises 5–18. x+0y+2z=11, x+0y+3z=14, x+2y−0z=5

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Textbook Question

In Exercises 1–4, determine if the given ordered triple is a solution of the system. (4, 1, 2) x−2y=2, 2x+3y=11, y−4z=−7

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Textbook Question

In Exercises 1–4, determine if the given ordered triple is a solution of the system. (2,−1, 3) x+ y+0z=4, x−2y−0z=1, 2x−y−2z=−1

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Textbook Question

Find the quadratic function y = ax^2 + bx + c whose graph passes through the points (1, 4), (3, 20), and (-2, 25).

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Textbook Question

Solve each system in Exercises 12–13. The is a piecewise function

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Textbook Question

Solve each problem. See Examples 5 and 9. The sum of the measures of the angles of any triangle is 180°. In a certain triangle, the largest angle measures 55° less than twice the medium angle, and the smallest angle measures 25° less than the medium angle. Find the measures of all three angles.

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Textbook Question

Solve each problem. See Examples 5 and 9. Solve the system of equations (4), (5), and (6) from Example 9. 25x + 40y + 20z = 2200 (4) 4x + 2y + 3z = 280 (5) 3x + 2y + z = 180 (6)

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Textbook Question

Solve each problem. See Examples 5 and 9. A cashier has a total of 30 bills, made up of ones, fives, and twenties. The number of twenties is 9 more than the number of ones. The total value of the money is $351. How many of each denomination of bill are there?

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Textbook Question

Solve each problem. See Examples 5 and 9. A sparkling-water distributor wants to make up 300 gal of sparkling water to sell for $6.00 per gallon. She wishes to mix three grades of water selling for $9.00, $3.00, and $4.50 per gallon, respectively. She must use twice as much of the $4.50 water as of the $3.00 water. How many gallons of each should she use?

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Textbook Question

Find the partial fraction decomposition of 4x²+5x-9/(x³- 6x-9)

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Textbook Question

Find the partial fraction decomposition for 1/x(x+1) and use the result to find the following sum:

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Textbook Question

In Exercises 43–46, perform each long division and write the partial fraction decomposition of the remainder term. (x^4-x^2+2)/(x^3-x^2)

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Textbook Question

In Exercises 43–46, perform each long division and write the partial fraction decomposition of the remainder term. (x^5+2)/(x^2-1)

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Textbook Question

In Exercises 9–42, write the partial fraction decomposition of each rational expression. (4x^2+3x+14)/(x^3 - 8)

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Textbook Question

In Exercises 9–42, write the partial fraction decomposition of each rational expression. (x^3-4x^2+9x-5)/(x^2 -2x+3)^2

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Textbook Question

In Exercises 9–42, write the partial fraction decomposition of each rational expression. x^3+x^2+2/(x² + 2)²

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Textbook Question

In Exercises 9–42, write the partial fraction decomposition of each rational expression. 6x^2-x+1/(x^3 + x²+x+1)

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Textbook Question

In Exercises 9–42, write the partial fraction decomposition of each rational expression. x+4/x² (x²+4)

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Textbook Question

In Exercises 9–42, write the partial fraction decomposition of each rational expression.5x^2+6x+3/(x + 1)(x² + 2x + 2)

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Textbook Question

In Exercises 9–42, write the partial fraction decomposition of each rational expression. 5x^2 -6x+7/(x − 1) (x² + 1)

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Textbook Question

In Exercises 9–42, write the partial fraction decomposition of each rational expression. x^2/(x − 1)² (x + 1)

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Textbook Question

In Exercises 9–42, write the partial fraction decomposition of each rational expression. x²+2x+7/x(x − 1)^2

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In Exercises 9–42, write the partial fraction decomposition of each rational expression. (x^2-6x+3)/(x − 2)³

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Textbook Question

In Exercises 9–42, write the partial fraction decomposition of each rational expression. (6x-11)/(x − 1)²

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Textbook Question

In Exercises 9–42, write the partial fraction decomposition of each rational expression. (2x^2 -18x -12)/x³- 4x

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Textbook Question

In Exercises 9–42, write the partial fraction decomposition of each rational expression. 4x² - 7x - 3/(x^3 -x)

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In Exercises 9–42, write the partial fraction decomposition of each rational expression. 4x^2+13x-9/x (x − 1)(x+3)

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Textbook Question

In Exercises 9–42, write the partial fraction decomposition of each rational expression. x/(x^2 +2x -3)

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In Exercises 9–42, write the partial fraction decomposition of each rational expression. 4/(2x^2 -5x -3)

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Textbook Question

In Exercises 9–42, write the partial fraction decomposition of each rational expression. 9x+21/(x² + 2x - 15)

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In Exercises 9–42, write the partial fraction decomposition of each rational expression. (7x-4)/(x^2-x-12)

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In Exercises 9–42, write the partial fraction decomposition of each rational expression. (3x +50)/(x -9)(x +2)

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Textbook Question

In Exercises 9–42, write the partial fraction decomposition of each rational expression. 1/x(x-1)

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In Exercises 9–42, write the partial fraction decomposition of each rational expression. x/(x-2)(x-3)

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Textbook Question

In Exercises 1–8, write the form of the partial fraction decomposition of the rational expression. It is not necessary to solve for the constants. (7x^2 -9x+3)/(x²+7)²

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Textbook Question

In Exercises 1–8, write the form of the partial fraction decomposition of the rational expression. It is not necessary to solve for the constants. x^3 + x² /(x² + 4)^2

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Textbook Question

In Exercises 1–8, write the form of the partial fraction decomposition of the rational expression. It is not necessary to solve for the constants. 5x²-6x+7 /(x − 1) (x² + 1)

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Textbook Question

In Exercises 1–8, write the form of the partial fraction decomposition of the rational expression. It is not necessary to solve for the constants. (3x+16)/(x + 1) (x − 2)²

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In Exercises 1–8, write the form of the partial fraction decomposition of the rational expression. It is not necessary to solve for the constants. (6x^2-14x-27)/(x+2) (x − 3)^2

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In Exercises 1–8, write the form of the partial fraction decomposition of the rational expression. It is not necessary to solve for the constants.(11x - 10)/(x − 2) (x + 1)

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Textbook Question

Exercises 57–59 will help you prepare for the material covered in the next section. Add: (5x−3)/(x^2+1) + 2x/(x^2+1)^2.

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Exercises 57–59 will help you prepare for the material covered in the next section. Subtract: 3/(x−4) − 2/(x+2).

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Textbook Question

In Exercises 16–24, write the partial fraction decomposition of each rational expression. (4x^3 + 5x^2 + 7x - 1)/(x^2 + x + 1)^2

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Textbook Question

In Exercises 16–24, write the partial fraction decomposition of each rational expression. (7x^2 - 7x + 23)/(x - 3)(x^2 + 4)

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Textbook Question

In Exercises 16–24, write the partial fraction decomposition of each rational expression.3x/(x - 2)(x^2 + 1)

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Textbook Question

In Exercises 16–24, write the partial fraction decomposition of each rational expression. (4x^2 - 3x - 4)/x(x + 2)(x - 1)

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Textbook Question

In Exercises 16–24, write the partial fraction decomposition of each rational expression. x/(x - 3)(x + 2)

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Textbook Question

Answer each question. By what expression should we multiply each side of 5/((3x(2x + 1)) = A/(3x) + B/(2x + 1) so that there are no fractions in the equation?

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Textbook Question

Answer each question. By what expression should we multiply each side of (3x - 2)/(x + 4)(3x^2 + 1) = A/(x + 4) + (Bx + C)/(3x^2 + 1) so that there are no fractions in the equation?

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Textbook Question

Answer each question. By what expression should we multiply each side of (3x - 1)/(x(2x^2 + 1)^2) = A/x + (Bx + C)/(2x^2 + 1) + (Dx + E)/(2x^2 + 1)^2 so that there are no fractions in the equation?

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Textbook Question

Find the partial fraction decomposition for each rational expression. See Examples 1–4. 5/(3x(2x + 1))

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Find the partial fraction decomposition for each rational expression. See Examples 1–4. (4x + 2)/((x + 2)(2x - 1))

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Textbook Question

Find the partial fraction decomposition for each rational expression. See Examples 1–4. x/(x^2 + 4x - 5)

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Find the partial fraction decomposition for each rational expression. See Examples 1–4. 4/(x(1 - x))

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Textbook Question

Find the partial fraction decomposition for each rational expression. See Examples 1–4. (4x^2 - x - 15)/(x(x + 1)(x - 1))

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Textbook Question

Find the partial fraction decomposition for each rational expression. See Examples 1–4. (2x + 1)/(x + 2)^3

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Textbook Question

Find the partial fraction decomposition for each rational expression. See Examples 1–4. (x^2)/(x^2 + 2x + 1)

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Find the partial fraction decomposition for each rational expression. See Examples 1–4. (x^3 + 4)/(9x^3 - 4x)

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Find the partial fraction decomposition for each rational expression. See Examples 1–4. (-3)/(x^2(x^2 + 5))

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Find the partial fraction decomposition for each rational expression. See Examples 1–4. (3x - 2)/((x + 4)(3x^2 + 1))

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Textbook Question

Find the partial fraction decomposition for each rational expression. See Examples 1–4. 1/(x(2x + 1)(3x^2 + 4))

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Find the partial fraction decomposition for each rational expression. See Examples 1–4. (2x^5 + 3x^4 - 3x^3 - 2x^2 + x)/(2x^2 + 5x + 2)

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Textbook Question

Find the partial fraction decomposition for each rational expression. See Examples 1–4. (3x - 1)/(x(2x^2 + 1)^2)

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Find the partial fraction decomposition for each rational expression. See Examples 1–4. (-x^4 - 8x^2 + 3x - 10)/((x + 2)(x^2 + 4)^2)

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Find the partial fraction decomposition for each rational expression. See Examples 1–4. (x^2)/(x^4 - 1)

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Textbook Question

Find the partial fraction decomposition for each rational expression. See Examples 1–4. (4x^2 - 3x - 4)/(x^3 + x^2 - 2x)

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Find the partial fraction decomposition for each rational expression. 5-2x / (x^2 + 2)(x - 1)

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Textbook Question

In Exercises 1 - 24, use Gaussian Eliminaion to find the complete solution to each system of equations, or show that none exists. w + 2x + 3y - z = 7 2x - 3y + z = 4 w - 4x + y = 3

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Textbook Question

In Exercises 1 - 24, use Gaussian Eliminaion to find the complete solution to each system of equations, or show that none exists. w + x - y + z = - 2 2w - x + 2y - z = 7 - w + 2x + y + 2z = - 1

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Textbook Question

In Exercises 1 - 24, use Gaussian Eliminaion to find the complete solution to each system of equations, or show that none exists. x + y - 2z = 2 3x - y - 6z = - 7

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Textbook Question

In Exercises 1 - 24, use Gaussian Eliminaion to find the complete solution to each system of equations, or show that none exists. x + 2y + 3z = 5 y - 5z = 0

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Textbook Question

In Exercises 1 - 24, use Gaussian Eliminaion to find the complete solution to each system of equations, or show that none exists. 2x + y - z = 2 3x + 3y - 2z = 3

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Textbook Question

In Exercises 1 - 24, use Gaussian Eliminaion to find the complete solution to each system of equations, or show that none exists. w - 3x + y - 4z = 4 - 2w + x + 2y = - 2 3w - 2x + y - 6z = 2 - w + 3x + 2y - z = - 6

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Textbook Question

In Exercises 1 - 24, use Gaussian Eliminaion to find the complete solution to each system of equations, or show that none exists. 2w + x - y = 3 w - 3x + 2y = - 4 3w + x - 3y + z = 1 w + 2x - 4y - z = - 2

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Textbook Question

In Exercises 1 - 24, use Gaussian Eliminaion to find the complete solution to each system of equations, or show that none exists. w - 2x - y - 3z = - 9 w + x - y = 0 3w + 4x + z = 6 2x - 2y + z = 3

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Textbook Question

In Exercises 1 - 24, use Gaussian Eliminaion to find the complete solution to each system of equations, or show that none exists. 8x + 5y + 11z = 30 - x - 4y + 2z = 3 2x - y + 5z = 12

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Textbook Question

In Exercises 1 - 24, use Gaussian Eliminaion to find the complete solution to each system of equations, or show that none exists. 3x + 4y + 2z = 3 4x - 2y - 8z = - 4 x + y - z = 3

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Textbook Question

In Exercises 1 - 24, use Gaussian Eliminaion to find the complete solution to each system of equations, or show that none exists. 5x + 8y - 6z = 14 3x + 4y - 2z = 8 x + 2y - 2z = 3

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Textbook Question

In Exercises 1 - 24, use Gaussian Eliminaion to find the complete solution to each system of equations, or show that none exists. 5x + 12y + z = 10 2x + 5y + 2z = - 1 x + 2y - 3z = 5

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Textbook Question

In Exercises 8–11, use Gaussian elimination to find the complete solution to each system, or show that none exists.

176

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Textbook Question

In Exercises 8–11, use Gaussian elimination to find the complete solution to each system, or show that none exists.

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Textbook Question

In Exercises 8–11, use Gaussian elimination to find the complete solution to each system, or show that none exists.

126

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7. Systems of Equations & Matrices

Introduction to Matrices

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