7. Systems of Equations & Matrices

Evaluate each determinant. See Example 3.

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

Evaluate each determinant. See Example 3.

In Exercises 23–30, use expansion by minors to evaluate each determinant. 0.5 7 50.5 3 90.5 1 3

In Exercises 31–36, use the alternative method for evaluating third-order determinants on here to evaluate each determinant. - 3 4 - 55 - 2 08 - 1 3

In Exercises 31–36, use the alternative method for evaluating third-order determinants on here to evaluate each determinant. 1 5 61 4 51 9 10

In Exercises 31–36, use the alternative method for evaluating third-order determinants on here to evaluate each determinant. 0.5 7 50.5 3 90.5 1 3

Evaluate each determinant.

In Exercises 37–44, use Cramer's Rule to solve each system. x + y + z = 02x - y + z = - 1- x + 3y - z = - 8

Evaluate each determinant.

In Exercises 37–44, use Cramer's Rule to solve each system. 4x - 5y - 6z = - 1x - 2y - 5z = - 122x - y = 7

Evaluate each determinant.

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

In Exercises 37–44, use Cramer's Rule to solve each system. x + 2z = 102y - z = - 52x + 3y = 13

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 = 42x + 3y - 2z = 62x - 9y + 6z = 2