7. Systems of Equations & Matrices

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

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

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|

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

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 methodto determine the solution set. See Examples 5–7. x + y = 4 2x - y = 2

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

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

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

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

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

Use Cramer's rule to solve each system of equations. If D = 0, then use another methodto determine the solution set. See Examples 5–7. 2x - y + 4z = -23x + 2y - z = -3x + 4y + 2z = 17

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

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