7. Systems of Equations & Matrices

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

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.

$5x+4y=10$

$5x+4y=10$

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. 1.5

x + 3y = 5

2x + 4y = 3

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

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

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

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

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