7. Systems of Equations & Matrices

Introduction to Matrices

College Algebra

7. Systems of Equations & Matrices

Introduction to Matrices

6:41 minutes

Problem 43b

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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First, identify the dimensions of matrices B and C. Matrix B is 2x2 and matrix C is 2x2.

Check if the multiplication BC is defined. Since the number of columns in B (2) matches the number of rows in C (2), BC is defined.

Perform the matrix multiplication BC. Multiply each element of the rows of B by the corresponding elements of the columns of C and sum them up.

Next, identify the dimensions of matrix A, which is 3x2, and the resulting matrix BC, which will be 2x2.

Check if the multiplication A(BC) is defined. Since the number of columns in A (2) matches the number of rows in BC (2), A(BC) is defined.

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Textbook Question

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Textbook Question

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Textbook Question

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Textbook Question

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Textbook Question

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Textbook Question

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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 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.

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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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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 $R_1\leftrightarrow R_2$

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Multiple Choice

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.

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