7. Systems of Equations & Matrices

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

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 1A = B = 0 1 - 1 0 0 1 0 11 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 1/2A = 1 3 4 B = - 1/2 0 1/21 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 1A = 0 0 1 B = 1 0 01 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 = - 3x - y + z = 4- w + x - y + 2z = 2- x + y - 2z = - 4The inverse of is

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 = 82y - z = - 72x + 3y = 1The inverse of is

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 = 82x + 7y + 6z = 102x + 7y + 7z = 9The inverse of is

In Exercises 1 - 12, find the products AB and BA to determine whether B is the multiplicative inverse of A. - 2 1 1 2A = B = 3/2 - 1/2 3 4

In Exercises 1 - 12, find the products AB and BA to determine whether B is the multiplicative inverse of A. - 4 0 - 2 4A = B = 1 3 0 1

In Exercises 1 - 12, find the products AB and BA to determine whether B is the multiplicative inverse of A. 4 - 3 4 3A = B = - 5 4 5 4

In Exercises 33 - 36, write each matrix equation as a system of linear equations without matrices.

In Exercises 33 - 36, write each matrix equation as a system of linear equations without matrices.

In Exercises 13 - 18, use the fact that ifa b d - bA = then A^(-1) = 1/(ad-bc) to find the inverse of c d - c aeach matrix, if possible. Check that AA^(-1) = I_2 and A^(-1)A = I_2. 10 - 2A = - 5 1

In Exercises 13 - 18, use the fact that ifa b d - bA = then A^(-1) = 1/(ad-bc) to find the inverse of c d - c aeach matrix, if possible. Check that AA^(-1) = I_2 and A^(-1)A = I_2. 3 - 1A = - 4 2