College Algebra, 4th Edition

Practice Test A

1. Give the order of the matrix and the value of the designated entry of the matrix.

   $$\left[\begin{array}{rrrr}3& -1& -3& 0\\ 2& 4& 1& 7\\ 5& 0& 3& 2\\ 8& 10& 9& 6\\ -4& 0& 0& 3\end{array}\right]a_{43}$$

2. Write an augmented matrix for the system of equations.

   $$\{\begin{array}{rclrrll}7x& -& 3y& +& 9z& =& 5\\ -2x& +& 4y& +& 3z& =& -12\\ 8x& -& 5y& +& z& =& -9\end{array}$$

3. Write the system of linear equations represented by the augmented matrix

   $$\left[\begin{array}{rrrr}4& 0& -1& -3\\ 1& 3& 0& 9\\ 2& 7& 5& 8\end{array}\right].$$

   Use x, y, and z for the variables.

4. Find values for the variables so that the matrices

   $$\left[\begin{array}{rrrrrr}x& -& 5& y& +& 3\\ z& 9\end{array}\right]=\left[\begin{array}{rr}5& 13\\ 0& 9\end{array}\right]$$

   are equal.

In Problems 5 and 6, solve the system of equations by using matrices.

5. $\{\begin{array}{rcrrrll}x& +& 2y& +& z& =& 6\\ x& +& y& -& z& =& 7\\ 2x& -& y& +& 2z& =& -3\end{array}$

6. $\{\begin{array}{rcrrrll}2x& +& y& -& 4z& =& 6\\ -x& +& 3y& -& z& =& -2\\ 2x& -& 6y& +& 2z& =& 4\end{array}$

7. Let $A=\left[\begin{array}{rr}5& -2\\ 4& 0\\ 7& 6\end{array}\right]\text{ and }B=\left[\begin{array}{rr}-3& -1\\ 0& -8\\ -4& 6\end{array}\right].$ Find $A-B.$

In Problems 8 and 9, find the product AB or state that AB is not defined.

8. $A=\left[\begin{array}{rrr}3& -7& 2\end{array}\right],B=\left[\begin{array}{r}0\\ 1\\ 4\end{array}\right]$

9. $A=\left[\begin{array}{rrr}-4& 1& 2\\ -9& 0& 3\end{array}\right],B=\left[\begin{array}{rr}2& 8\\ 7& -5\end{array}\right]$

For Problems 10–13, let

$$A=[\begin{array}{rr}-3& 1\end{array}$$