Name:    Chapter 7 Post Test

1.

Select the augmented matrix for the system of linear equations.

 a. b. c. d. e.

2.

Fill in the blank(s) using elementary row operations to form a row-equivalent matrix.

 a. b. c. d. e.

3.

Write the augmented matrix for the system of linear equations.

 a. b. c. d. e.

4.

Fill in the blank using elementary row operations to form a row-equivalent matrix.

 a. b. c. d. e.

5.

Determine whether the two systems of linear equations yield the same solutions. If so, find the solutions using matrices.

 a. x = –3, y = –6, z = 2 b. The systems yield different solutions. c. x = 3, y = 2, z = –3 d. x = 3, y = 6, z = 2 e. x = –6, y = 2, z = –3

6.

Find .

 a. b. c. d. e.

7.

Evaluate the expression.

 a. b. c. d. e.

8.

Evaluate the expression.

 a. b. c. not possible d. e.

9.

Solve for X in the equation given.

 a. b. c. d. e.

10.

Find the inverse of the matrix .
 a. b. c. d. e.

11.

Find the inverse of the matrix (if it exists).
 a. b. does not exist c. d. e.

12.

Use the matrix capabilities of a graphing utility to solve the following system of linear equations:

 a. b. c. d. e.

13.

Find all the cofactors of  the matrix.

 a. b. c. d. e.

14.

Find the determinant of the matrix by the method of expansion by cofactors. Expand using the column 2.

 a. –423 b. 423 c. –421 d. –422 e. –424

15.

Find .

 a. –7 b. –8 c. –6 d. –5 e. –4

16.

Use the matrix capabilities of a graphing utility to find the determinant of the matrix
.
 a. –432 b. c. d. –1080 e.

17.

Use a graphing utility and Cramer’s Rule to solve (if possible) the system of equations.

 a. b. c. d. e.

18.

Use Crammer’s Rule to solve (if possible) the system of equations.

 a. b. c. d. e.

19.

Find a value of such that the triangle with the given vertices has an area of 4 square units.

 a. or b. or c. or d. or e. or

20.

Use a determinant to determine whether the points and are collinear.
 a. ; therefore, the points are not collinear. b. ; therefore, the points are collinear.