7. Systems of Equations & Matrices

Determinants and Cramer's Rule

7. Systems of Equations & Matrices

Determinants and Cramer's Rule

Guided videos.

Learn with Patrick

Go to the course

Guided course

4:36

Determinants of 2×2 Matrices

Cramer's Rule - 2 Equations with 2 Unknowns

Determinants of 3×3 Matrices

Cramer's Rule - 3 Equations w/ 3 Unknowns

Additional 1 creators.

Learn with other creators

Ex: Find the Value of a 4x4 Determinant Using Cofactor Expansion (with Zeros)

05:08

Ex: Find the Value of a 4x4 Determinant Using Cofactor Expansion (with Zeros)

Evaluate the Determinant of a 4x4 Matrix

Determinant of a 4X4 Matrix

How To Find The Determinant of a 4x4 Matrix

The Organic Chemistry Tutor

1445

views

Practice this topic

Multiple Choice

Evaluate the determinant of the matrix.

137

views

Multiple Choice

Write each equation in standard form and use Cramer's Rule to solve the system.

$y=-3x+4$

$-2x=7y-9$

176

views

Multiple Choice

Evaluate the determinant of the matrix.

200

views

Multiple Choice

Solve the system of equations using Cramer's Rule.

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

$x+y+z=3$

$5x+y+2z=5$

141

views

Multiple Choice

Write each equation in standard form and use Cramer's Rule to solve the system.

$y-9x=-3$

$-3x=4y-1$

139

views

Textbook Question

What is the value of ?

158

views

Textbook Question

Evaluate each determinant in Exercises 1–10. 5 7 2 3

182

views

Textbook Question

What expression in x represents ?

152

views

Textbook Question

Evaluate each determinant in Exercises 1–10. - 4 1 5 6

190

views

Textbook Question

Evaluate each determinant in Exercises 1–10. - 7 14 2 - 4

169

views

Textbook Question

What is the value of x if = 9?

137

views

Textbook Question

Evaluate each determinant. See Example 1.

146

views

Textbook Question

Evaluate each determinant in Exercises 1–10. - 5 - 1 - 2 - 7

159

views

Textbook Question

Evaluate each determinant in Exercises 1–10. - 5 - 1 - 2 - 7

159

views

Textbook Question

Evaluate each determinant. See Example 1.

156

views

Textbook Question

Evaluate each determinant in Exercises 1–10. 1/2 1/2 1/8 - 3/4

168

views

Textbook Question

For Exercises 11–22, use Cramer's Rule to solve each system. x + y = 7 x - y = 3

Evaluate each determinant. See Example 1.

146

views

Textbook Question

Evaluate each determinant. See Example 1.

135

views

Textbook Question

For Exercises 11–22, use Cramer's Rule to solve each system. 12x + 3y = 15 2x - 3y = 13

192

views

Textbook Question

For Exercises 11–22, use Cramer's Rule to solve each system. 12x + 3y = 15 2x - 3y = 13

192

views

Textbook Question

Evaluate each determinant. See Example 1.

147

views

Textbook Question

For Exercises 11–22, use Cramer's Rule to solve each system. 4x - 5y = 17 2x + 3y = 3

198

views

Textbook Question

For Exercises 11–22, use Cramer's Rule to solve each system. x + 2y = 3 3x - 4y = 4

248

views

Textbook Question

Find the cofactor of each element in the second row of each matrix. See Example 2.

157

views

Textbook Question

Find the cofactor of each element in the second row of each matrix. See Example 2.

199

views

Textbook Question

For Exercises 11–22, use Cramer's Rule to solve each system. 3x - 4y = 4 2x + 2y = 12

202

views

Textbook Question

For Exercises 11–22, use Cramer's Rule to solve each system. 3x - 4y = 4 2x + 2y = 12

202

views

Textbook Question

Evaluate each determinant. See Example 3.

142

views

Textbook Question

For Exercises 11–22, use Cramer's Rule to solve each system. 2x = 3y + 2 5x = 51 - 4y

207

views

Textbook Question

In Exercises 23–30, use expansion by minors to evaluate each determinant. 3 0 0 2 1 - 5 2 5 - 1

172

views

Textbook Question

Evaluate each determinant. See Example 3.

130

views

Textbook Question

Evaluate each determinant. See Example 3.

169

views

Textbook Question

In Exercises 23–30, use expansion by minors to evaluate each determinant. 3 1 0 - 3 4 0 - 1 3 - 5

184

views

Textbook Question

In Exercises 23–30, use expansion by minors to evaluate each determinant. 3 1 0 - 3 4 0 - 1 3 - 5

184

views

Textbook Question

Evaluate each determinant. See Example 3.

145

views

Textbook Question

In Exercises 23–30, use expansion by minors to evaluate each determinant. 1 1 1 2 2 2 - 3 4 - 5

160

views

Textbook Question

In Exercises 23–30, use expansion by minors to evaluate each determinant. 0.5 7 5 0.5 3 9 0.5 1 3

175

views

Textbook Question

In Exercises 31–36, use the alternative method for evaluating third-order determinants on here to evaluate each determinant. - 3 4 - 5 5 - 2 0 8 - 1 3

200

views

Textbook Question

In Exercises 31–36, use the alternative method for evaluating third-order determinants on here to evaluate each determinant. - 3 4 - 5 5 - 2 0 8 - 1 3

200

views

Textbook Question

In Exercises 31–36, use the alternative method for evaluating third-order determinants on here to evaluate each determinant. 1 5 6 1 4 5 1 9 10

183

views

Textbook Question

In Exercises 31–36, use the alternative method for evaluating third-order determinants on here to evaluate each determinant. 0.5 7 5 0.5 3 9 0.5 1 3

169

views

Textbook Question

Evaluate each determinant.

252

views

Textbook Question

In Exercises 37–44, use Cramer's Rule to solve each system. x + y + z = 0 2x - y + z = - 1 - x + 3y - z = - 8

166

views

Textbook Question

In Exercises 37–44, use Cramer's Rule to solve each system. x + y + z = 0 2x - y + z = - 1 - x + 3y - z = - 8

166

views

Textbook Question

Evaluate each determinant.

192

views

Textbook Question

In Exercises 37–44, use Cramer's Rule to solve each system. 4x - 5y - 6z = - 1 x - 2y - 5z = - 12 2x - y = 7

298

views

Textbook Question

Evaluate each determinant.

192

views

Textbook Question

In Exercises 37–44, use Cramer's Rule to solve each system. x + y + z = 4 x - 2y + z = 7 x + 3y + 2z = 4

223

views

Textbook Question

In Exercises 37–44, use Cramer's Rule to solve each system. x + 2z = 10 2y - z = - 5 2x + 3y = 13

254

views

Textbook Question

In Exercises 37–44, use Cramer's Rule to solve each system. x + 2z = 10 2y - z = - 5 2x + 3y = 13

254

views

Textbook Question

In Exercises 45–48, explain why the system of equations cannot be solved using Cramer's Rule. Then use Gaussian elimination to solve the system. 2x - 3y + 2z = 4 2x + 3y - 2z = 6 2x - 9y + 6z = 2

270

views

Textbook Question

In Exercises 46–51, evaluate each determinant.

307

views

Textbook Question

In Exercises 45–48, explain why the system of equations cannot be solved using Cramer's Rule. Then use Gaussian elimination to solve the system. 4x - 3y - 2z = 12 8x - 6y - 4z = 22

207

views

Textbook Question

Use the determinant theorems to evaluate each determinant. See Example 4.

161

views

Textbook Question

Solve each equation. = 8

128

views

Textbook Question

Solve each equation. = 2x

155

views

Textbook Question

Evaluate each determinant in Exercises 49–52. 4 2 8 - 7 - 2 0 4 1 5 0 0 5 4 0 0 - 1

200

views

Textbook Question

In Exercises 46–51, evaluate each determinant.

192

views

Textbook Question

Evaluate each determinant in Exercises 49–52. 4 2 8 - 7 - 2 0 4 1 5 0 0 5 4 0 0 - 1

200

views

Textbook Question

Use the determinant theorems to evaluate each determinant. See Example 4.

139

views

Textbook Question

Evaluate each determinant in Exercises 49–52. - 2 - 3 3 5 1 - 4 0 0 1 2 2 - 3 2 0 1 1

182

views

Textbook Question

In Exercises 46–51, evaluate each determinant.

192

views

Textbook Question

Use the determinant theorems to evaluate each determinant. See Example 4.

128

views

Textbook Question

In Exercises 46–51, evaluate each determinant.

192

views

Textbook Question

In Exercises 53–54, evaluate each determinant. | | 3 1| |7 0| | | |- 2 3| |1 5| | | | | | 3 0| |9 - 6| | | | 0 7| |3 5| |

181

views

Textbook Question

In Exercises 52–55, use Cramer's Rule to solve each system.

253

views

Textbook Question

Use the determinant theorems to evaluate each determinant. See Example 4.

142

views

Textbook Question

In Exercises 52–55, use Cramer's Rule to solve each system.

253

views

Textbook Question

Use the determinant theorems to evaluate each determinant. See Example 4.

140

views

Textbook Question

In Exercises 55–56, write the system of linear equations for which Cramer's Rule yields the given determinants. 2 - 4 8 - 4 D = D_x = 3 5 - 10 5

429

views

Textbook Question

In Exercises 57–60, solve each equation for x. |- 2 x| | | = 32 | 4 6|

175

views

Textbook Question

Use the determinant theorems to evaluate each determinant. See Example 4.

In Exercises 57–60, solve each equation for x. |1 x - 2| |3 1 1| = - 8 |0 - 2 2|

171

views

Textbook Question

Use the determinant theorems to evaluate each determinant. See Example 4.

133

views

Textbook Question

In Exercises 57–60, solve each equation for x. |1 x - 2| |3 1 1| = - 8 |0 - 2 2|

171

views

Textbook Question

Use the determinant theorems to evaluate each determinant. See Example 4.

126

views

Textbook Question

Use Cramer's rule to solve each system of equations. If D = 0, then use another method to determine the solution set. See Examples 5–7. x + y = 4 2x - y = 2

255

views

Textbook Question

Use Cramer's rule to solve each system of equations. If D = 0, then use another method to determine the solution set. See Examples 5–7. 4x + 3y = -7 2x + 3y = -11

123

views

Textbook Question

Use Cramer's rule to solve each system of equations. If D = 0, then use another method to determine the solution set. See Examples 5–7. 5x + 4y = 10 3x - 7y = 6

143

views

Textbook Question

Use Cramer's rule to solve each system of equations. If D = 0, then use another method to determine the solution set. See Examples 5–7. 1.5x + 3y = 5 2x + 4y = 3

136

views

Textbook Question

Use Cramer's rule to solve each system of equations. If D = 0, then use another method to determine the solution set. See Examples 5–7. 3x + 2y = 4 6x + 4y = 8

125

views

Textbook Question

Use Cramer's rule to solve each system of equations. If D = 0, then use another method to determine the solution set. See Examples 5–7. (1/2)x + (1/3)y = 2 (3/2)x - (1/2)y = -12

172

views

Textbook Question

Use Cramer's rule to solve each system of equations. If D = 0, then use another method to determine the solution set. See Examples 5–7. 2x - y + 4z = -2 3x + 2y - z = -3 x + 4y + 2z = 17

182

views

Textbook Question

Use Cramer's rule to solve each system of equations. If D = 0, then use another method to determine the solution set. See Examples 5–7. x + 2y + 3z = 4 4x + 3y + 2z = 1 -x - 2y - 3z = 0

196

views

Textbook Question

Use Cramer's rule to solve each system of equations. If D = 0, then use another method to determine the solution set. See Examples 5–7. -2x - 2y + 3z = 4 5x + 7y - z = 2 2x + 2y - 3z = -4

161

views

Textbook Question

In Exercises 1 - 12, find the products AB and BA to determine whether B is the multiplicative inverse of A. 0 0 - 2 1 1 2 0 3 - 1 0 1 1 0 1 1 1 A = B = 0 1 - 1 0 0 1 0 1 1 0 0 - 1 1 2 0 2

views

Textbook Question

In Exercises 1 - 12, find the products AB and BA to determine whether B is the multiplicative inverse of A. 1 2 3 7/2 - 3 1/2 A = 1 3 4 B = - 1/2 0 1/2 1 4 3 - 1/2 1 - 1/2

views

Textbook Question

In Exercises 1 - 12, find the products AB and BA to determine whether B is the multiplicative inverse of A. 0 1 0 0 0 1 A = 0 0 1 B = 1 0 0 1 0 0 0 1 0

131

views

Textbook Question

In Exercises 37 - 42, a. Write each linear system as a matrix equation in the form AX = B. b. Solve the system using the inverse that is given for the coefficient matrix. w - x + 2y = - 3 x - y + z = 4 - w + x - y + 2z = 2 - x + y - 2z = - 4 The inverse of is

views

Textbook Question

In Exercises 37 - 42, a. Write each linear system as a matrix equation in the form AX = B. b. Solve the system using the inverse that is given for the coefficient matrix. x - y + z = 8 2y - z = - 7 2x + 3y = 1 The inverse of is

views

Textbook Question

In Exercises 37 - 42, a. Write each linear system as a matrix equation in the form AX = B. b. Solve the system using the inverse that is given for the coefficient matrix. 2x + 6y + 6z = 8 2x + 7y + 6z = 10 2x + 7y + 7z = 9 The inverse of is

views

Textbook Question

In Exercises 1 - 12, find the products AB and BA to determine whether B is the multiplicative inverse of A. - 2 1 1 2 A = B = 3/2 - 1/2 3 4

views

Textbook Question

In Exercises 1 - 12, find the products AB and BA to determine whether B is the multiplicative inverse of A. - 4 0 - 2 4 A = B = 1 3 0 1

views

Textbook Question

In Exercises 1 - 12, find the products AB and BA to determine whether B is the multiplicative inverse of A. 4 - 3 4 3 A = B = - 5 4 5 4

views

Textbook Question

In Exercises 33 - 36, write each matrix equation as a system of linear equations without matrices.

views

Textbook Question

In Exercises 33 - 36, write each matrix equation as a system of linear equations without matrices.

views

Textbook Question

In Exercises 29 - 32, write each linear system as a matrix equation in the form AX = B, where A is the coefficient matrix and B is the constant matrix. x + 3y + 4z = - 3 x + 2y + 3z = - 2 x + 4y + 3z = - 6

100

views

Textbook Question

In Exercises 29 - 32, write each linear system as a matrix equation in the form AX = B, where A is the coefficient matrix and B is the constant matrix. 6x + 5y = 13 5x + 4y = 10

104

views

Textbook Question

In Exercises 13 - 18, use the fact that if a b d - b A = then A^(-1) = 1/(ad-bc) to find the inverse of c d - c a each matrix, if possible. Check that AA^(-1) = I_2 and A^(-1)A = I_2. 10 - 2 A = - 5 1

views

Textbook Question

In Exercises 13 - 18, use the fact that if a b d - b A = then A^(-1) = 1/(ad-bc) to find the inverse of c d - c a each matrix, if possible. Check that AA^(-1) = I_2 and A^(-1)A = I_2. 3 - 1 A = - 4 2

views

Textbook Question

In Exercises 13 - 18, use the fact that if a b d - b A = then A^(-1) = 1/(ad-bc) to find the inverse of c d - c a each matrix, if possible. Check that AA^(-1) = I_2 and A^(-1)A = I_2. 2 3 A = - 1 2

views

Textbook Question

In Exercises 43–44, (a) Write each linear system as a matrix equation in the form AX = B (b) Solve the system using the inverse that is given for the coefficient matrix.

views

Textbook Question

In Exercises 39–42, find A^(-1) Check that AA^-1 = I and A^(-1)A = I

views

Textbook Question

In Exercises 37–38, find the products and to determine whether B is the multiplicative inverse of A.

views

Textbook Question

Answer each question. What is the product of [2x2 matrix] and I2 (in either order)?

views

Textbook Question

Answer each question. What is the product [3x3 matrix] [3x3 matrix]?

views

Textbook Question

Are the given matrices inverses of each other? (Hint: Check to see whether their products are the identity matrix I￬n.) [2x2 matrix] and [2x2 matrix]

views

Textbook Question

Are the given matrices inverses of each other? (Hint: Check to see whether their products are the identity matrix I￬n.) [3x3 matrix] and [3x3 matrix]

views

Textbook Question

Find the inverse, if it exists, for each matrix. [2x2 matrix]

views

Textbook Question

Find the inverse, if it exists, for each matrix. [2x2 matrix]

views

Textbook Question

Find the inverse, if it exists, for each matrix. [2x2 matrix]

views

Textbook Question

Find the inverse, if it exists, for each matrix. [3x3 matrix]

views

Textbook Question

Find the inverse, if it exists, for each matrix. [3x3 matrix]

views

Textbook Question

Find the inverse, if it exists, for each matrix. [3x3 matrix]

views

Showing 115 of 115 practice

My Courses

Chemistry

Biology

Math

Physics

Business

Social Sciences

Programming

Product & Marketing

7. Systems of Equations & Matrices

Determinants and Cramer's Rule

Learn with Patrick

Learn with other creators

Practice this topic