Exam 9: Matrices and Determinants

Use the determinant feature of a graphing calculator to solve the system by Cramer's rule . (Round to one decimal place.) -1.5x + 3.1y - 2.3z + 0.6w = 2.7 6.1x - 0.5z - 3.4w = 0.8 11.5y - 2.2w = 0 4.0x + 3.0y - 2.1z = 9

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. -

Solve the system using Gaussian elimination. --3x - y - 9z = -67 6x + 8y - 3z = 50 2x - 5y + z = -25

Find the product. -

Determine whether the matrices in each pair are inverses of each other. -

Given matrices A and B, find the indicated matrix if possible. - Find AB.

Solve the problem. -The sum of a student's three scores is 231. If the first is 14 points more than the second, and the sum of the first two is 24 more than twice the third, what was the first score?

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

Perform the indicated operation, if possible. -

Find the product. -

Find the product. -

Provide an appropriate response. -Which of the following properties do not hold for matrix multiplication? (i) Associative property (ii) Commutative property (iii) Distributive property (iv) Zero-factor property (If the product of two matrices is a Zero matrix, one of the factors must be a zero matrix.)

Write the augmented matrix for the system. -

Perform the indicated row operation on the given augmented matrix. -

Find the product. -

Solve the problem. -At a store, Sam bought 6 batteries, 14 60-watt light bulbs, 48 100-watt light bulbs, 5 picture-hanging kits, and a hammer. Jennifer bought 8 batteries, 6 100-watt light bulbs, and a package of tacks. Write the information as a 2 X 6 matrix.

Determine the size of the matrix. -

Use Cramer's rule to solve the system. -0.8x + 0.05y = 580 x - y = 300

Determine whether the matrices in each pair are inverses of each other. -

Given matrices A and B, find the indicated matrix if possible. - Find AB.