Name:    Chapter 7 Pre Test

1.

Select the augmented matrix for the system of linear equations.

 a. b. c. d. e.

2.

Use matrices to find the system of equations (if possible). Use Gaussian elimination with
back-substitution or Gauss-Jordan elimination.

 a. b. c. d. e.

3.

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

 a. b. c. d. e.

4.

An augmented matrix that represents a system of linear equations (in variables x, y, and z) has been reduced using Gauss-Jordan elimination. Write the solution represented by the augmented matrix.

 a. x = 0, y = 0, z = 0 b. x = –5x, y = –4y, z = –3z c. x = –5, y = –3, z = –4 d. x = 5, y = 3, z = 4 e. x = –5, y = 0, z = 0

5.

Use matrices to solve the system of equations (if possible). Use Gaussian elimination with back-substitution or Gauss-Jordan elimination.

 a. x = 5, y = –1 b. x = 1, y = –5 c. x = –1, y = 5 d. x = 5, y = 1 e. no solution

6.

Use matrices to solve the system of equations (if possible). Use Gaussian elimination with back-substitution or Gauss-Jordan elimination.

 a. x = –5, y = –3, z = 2 b. x = 3, y = –5, z = –2 c. x = 5, y = –3, z = 2 d. no solution e. x = 5, y = 3, z = 2

7.

Find .

 a. b. c. d. e.

8.

If possible, find and state the order of the result.

 a. b. c. d. e.

9.

Write the system of linear equations as a matrix equation, .

 a. b. c. d. e.

10.

Use the inverse formula to find the inverse of the matrix (if it exists).

 a. b. c. d. e.

11.

Use the inverse formula   to find the inverse of the matrix (if it exists).

 a. Does not exist b. c. d. e.

12.

Use the inverse formula to find the inverse of the matrix (if it exists).

 a. b. c. d. e.

13.

Find all the cofactors of the matrix.

 a. b. c. d. e.

14.

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

15.

Evaluate the determinant of the matrix below to determine which of the following makes the equation true.

 a. b. c. d. e.

16.

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

 a. b. c. d. e.

17.

Find a value of such that the triangle with the given vertices has an area of 6 square units.

 a. –2 or b. –2 or c. –2 or d. 2 or e. 2 or

18.

Use determinants to find the area of a triangle with given vertices and confirm your answer by plotting the points in a coordinate plane and using the formula
Area = .

 a. 28 b. 20 c. 22 d. 26 e. 24

19.

Use a determinant and the given vertices of a triangle to find the area of the triangle.

 a. b. 4 c. d. e.

20.

Use a determinant and the given vertices of a triangle to find the area of the triangle.

 a. b. 4 c. d. e. 14