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

1648

views

Practice this topic

Multiple Choice

Evaluate the determinant of the matrix.

168

views

Multiple Choice

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

$y=-3x+4$

$-2x=7y-9$

209

views

Multiple Choice

Evaluate the determinant of the matrix.

248

views

Multiple Choice

Solve the system of equations using Cramer's Rule.

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

$x+y+z=3$

$5x+y+2z=5$

167

views

Multiple Choice

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

$y-9x=-3$

$-3x=4y-1$

170

views

Textbook Question

What is the value of ?

181

views

Textbook Question

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

199

views

Textbook Question

What expression in x represents ?

176

views

Textbook Question

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

213

views

Textbook Question

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

189

views

Textbook Question

What is the value of x if = 9?

163

views

Textbook Question

Evaluate each determinant. See Example 1.

166

views

Textbook Question

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

193

views

Textbook Question

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

193

views

Textbook Question

Evaluate each determinant. See Example 1.

178

views

Textbook Question

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

191

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.

162

views

Textbook Question

Evaluate each determinant. See Example 1.

155

views

Textbook Question

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

217

views

Textbook Question

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

217

views

Textbook Question

Evaluate each determinant. See Example 1.

160

views

Textbook Question

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

224

views

Textbook Question

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

285

views

Textbook Question

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

187

views

Textbook Question

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

247

views

Textbook Question

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

227

views

Textbook Question

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

227

views

Textbook Question

Evaluate each determinant. See Example 3.

160

views

Textbook Question

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

228

views

Textbook Question

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

197

views

Textbook Question

Evaluate each determinant. See Example 3.

155

views

Textbook Question

Evaluate each determinant. See Example 3.

192

views

Textbook Question

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

206

views

Textbook Question

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

206

views

Textbook Question

Evaluate each determinant. See Example 3.

168

views

Textbook Question

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

183

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

199

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

239

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

239

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

212

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

187

views

Textbook Question

Evaluate each determinant.

299

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

188

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

188

views

Textbook Question

Evaluate each determinant.

226

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

331

views

Textbook Question

Evaluate each determinant.

218

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

263

views

Textbook Question

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

295

views

Textbook Question

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

295

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

299

views

Textbook Question

In Exercises 46–51, evaluate each determinant.

345

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

250

views

Textbook Question

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

190

views

Textbook Question

Solve each equation. = 8

144

views

Textbook Question

Solve each equation. = 2x

175

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

224

views

Textbook Question

In Exercises 46–51, evaluate each determinant.

218

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

224

views

Textbook Question

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

165

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

211

views

Textbook Question

In Exercises 46–51, evaluate each determinant.

215

views

Textbook Question

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

151

views

Textbook Question

In Exercises 46–51, evaluate each determinant.

215

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| |

198

views

Textbook Question

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

284

views

Textbook Question

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

167

views

Textbook Question

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

284

views

Textbook Question

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

156

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

492

views

Textbook Question

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

202

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|

200

views

Textbook Question

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

154

views

Textbook Question

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

200

views

Textbook Question

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

149

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

313

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

147

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

166

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

159

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

152

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

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 - y + 4z = -2 3x + 2y - z = -3 x + 4y + 2z = 17

216

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

238

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

192

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

165

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

124

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

133

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