Chapter 8 Test REVIEW

Name______________________________________ Date ________________ Period _______ Row _____ Pre Calculus Chapter 8 Test REVIEW Write the system of linear equations represented by the 5) x + 3y + 2z = 11 augmented matrix. Use x, y, z, and, if necessary, w for the 4y + 9z = -12 variables. x + 7y + 11z = - 1 2 6 3 -2 1) 9 0 6 4 6 7 0 2

Write an augmented matrix for the system of equations. 2) 7x + 4z = 65 5y + 7z = 23 7x + 2y + 9z = 83

Perform the indicated matrix operations. -1 4 72 6) Let A = 0 4 and B = 17 4 . Find A - B. 6 -4 32

Solve the system of equations using matrices. Use Gaussian elimination with back-substitution. 3) 4x - y - 7z = 17 -6x - 7z = -68 6y + z = 32

-2 -4 7) A = -1 -6 -4 -1

and B =

-4 3 1 -6 . Find A + B. 3 -4

Use Gaussian elimination to find the complete solution to the system of equations, or state that none exists. 4) x + 8y + 8z = 8 7x + 7y + z = 1 8x + 15y + 9z = -9 8) Let A = 2 3 26

1

and B =

0 4 . Find 2A + B. -1 6

Find the product, AB, if possible. 9) A = 3 -2 1 , B = 3 0 0 4 -1 -2 2

Use Cramer's rule to solve the system or to determine that the system is inconsistent or contains dependent equations. 14) -2x + 4y = 4 4y + 3x = 34

10) A = -1 3 , B = 0 -2 4 54 1 -3 2 Use Cramer's rule to solve the system. 15) 3x - 6y + 4z = 27 7x + 8y + 3z = 72 -8x - 2y - 9z = -111

Write the linear system as a matrix equation in the form AX = B, where A is the coefficient matrix and B is the constant matrix. 11) 5x + 6y = 68 9x - 2y = 20

Find the inverse of the matrix. 16) A = 5 4 2 3

Evaluate the determinant. 12) 3 4 99 1 0 0 17) A = 2 1 0 0 -2 1

125 13) 2 2 3 125

2