7. Systems of Equations & Matrices

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

In Exercises 46–51, evaluate each determinant.

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 = 128x - 6y - 4z = 22

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

Solve each equation. = 8

Solve each equation. = 2x

Evaluate each determinant in Exercises 49–52. 4 2 8 - 7- 2 0 4 15 0 0 54 0 0 - 1

In Exercises 46–51, evaluate each determinant.

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

Evaluate each determinant in Exercises 49–52. - 2 - 3 3 51 - 4 0 01 2 2 - 32 0 1 1

In Exercises 46–51, evaluate each determinant.

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

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