Exam 9: Matrices and Determinants

Solve the problem. -A company makes 3 types of cable. Cable A requires 3 black, 3 white, and 2 red wires. B requires 1 black, 2 white, and 1 red. C requires 2 black, 1 white, and 2 red. They used 95 black, 100 white and 80 red wires. How Many of each cable were made?

Solve the system using the inverse of the coefficient matrix of the equivalent matrix equation. -2x + 8y + 6z = 20 4x + 2y - 2z = -2 3x - y + z = 11

Find the values that make the equation true. -

Solve the system using the inverse of the coefficient matrix of the equivalent matrix equation. --3x - y + 3z = -9 9x + 6z = 69 2y + z = 16

Solve the system, using Cramer's rule, if possible. -

Write a system of equations associated with the augmented matrix. Do not try to solve. -

Solve the problem. -The sum of three numbers is -1. The first, minus the second, plus 5 times the third, is 15. The third, plus 5 times the first, plus the second, is -9. What are the numbers?

Solve the problem. -Carney and Dobler sell home and mortgage insurance. Their sales for the months of July and August are given in the matrices. Home Mortgage Find the matrix that would give the change in sales.

Find the indicated matrix. -Let A = [-4 2] and B = [1 0]. Find 3A + 4B.

Solve the system using Gaussian elimination. -

Find the indicated matrix. - Find 4A.

Find the determinant of the given matrix. -

Provide an appropriate response. -Let where b and c are nonzero constants. Find A-1.

Use the determinant feature of a graphing calculator to solve the system by Cramer's rule . (Round to one decimal place.) -2.6x - 0.7y + 5.3z - 3.4w = 2.9 6.5y + 0.7w = -1.8 4.0z - 2.2w = 1.5 4.9x + 0.6w = 3.2

Write the augmented matrix for the system. -

Determine the row operation that was used on the first matrix to obtain the second matrix. -

Find the indicated matrix. - Find 3A + B.

Find a matrix A and a column matrix B that describe the following tables involving credits and tuition costs. Find the matrix product AB, and interpret the significance of the entries of this product. -

Find the values that make the equation true. -

Find the indicated power of the matrix A. - .