Lial - College Algebra 13th Edition - Chapter 6

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Ch. 5 - Systems and Matrices

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Lial 13th Edition

Ch. 5 - Systems and Matrices

Section 5.6

Problem 59

Graph the solution set of each system of inequalities.

$2 x plus 3 y is less than or equal to 12$

$2 x + 3 y > - 6$

$3 x plus y is less than 4$

$x is greater than or equal to 0$

$y is greater than or equal to 0$

Problem 65

Graph the solution set of each system of inequalities.

$y \leq \log x$

$y \geq ∣ x - 2 ∣$

Section 5.7

Problem 1

Fill in the blank(s) to correctly complete each sentence. For the following statement to be true, the value of x must be ____, and the value of y must be ____.

$[\begin{matrix} 3 & - 6 \\ 5 & 1 \end{matrix}] = [\begin{matrix} x + 1 & - 6 \\ 5 & y + 1 \end{matrix}]$

Problem 5

If the dimension of matrix A is 3 $\times$ 2 and the dimension of matrix B is 2 $\times$ 6, then the dimension of AB is ____.

Problem 7

Find the dimension of each matrix. Identify any square, column, or row matrices.

$[\begin{matrix} - 4 & 8 \\ 2 & 3 \end{matrix}]$

Problem 8

Find the dimension of each matrix. Identify any square, column, or row matrices.

$[\begin{matrix} - 9 & 6 & 2 \\ 4 & 1 & 8 \end{matrix}]$

Problem 9

Find the dimension of each matrix. Identify any square, column, or row matrices.

$[\begin{matrix} - 6 & 8 & 0 & 0 \\ 4 & 1 & 9 & 2 \\ 3 & - 5 & 7 & 1 \end{matrix}]$

Problem 10

Find the dimension of each matrix. Identify any square, column, or row matrices.

$[\begin{matrix} 8 & - 2 & 4 & 6 & 3 \end{matrix}]$

Problem 11

Find the dimension of each matrix. Identify any square, column, or row matrices.

$[\begin{matrix} 2 \\ 4 \end{matrix}]$

Problem 13

Find the values of the variables for which each statement is true, if possible.

$[\begin{matrix} - 3 & a \\ b & 5 \end{matrix}] = [\begin{matrix} c & 0 \\ 4 & d \end{matrix}]$

Problem 15

Find the values of the variables for which each statement is true, if possible.

$[\begin{matrix} x + 2 & y - 6 \\ z - 3 & w + 5 \end{matrix}] = [\begin{matrix} - 2 & 8 \\ 0 & 3 \end{matrix}]$

Problem 17

Find the values of the variables for which each statement is true, if possible.

$[\begin{matrix} x & y & z \end{matrix}] = [\begin{matrix} 21 & 6 \end{matrix}]$

Problem 19

Find the values of the variables for which each statement is true, if possible.

$[\begin{matrix} 0 & 5 & x \\ - 1 & 3 & y + 2 \\ 4 & 1 & z \end{matrix}] = [\begin{matrix} 0 & w & 6 \\ - 1 & 3 & 0 \\ 4 & 1 & 8 \end{matrix}]$

Problem 21

Find the values of the variables for which each statement is true, if possible.

$[\begin{matrix} - 7 + z & 4 r & 8 s \\ 6 p & 2 & 5 \end{matrix}] + [\begin{matrix} - 9 & 8 r & 3 \\ 2 & 5 & 4 \end{matrix}] = [\begin{matrix} 2 & 36 & 27 \\ 20 & 7 & 12 a \end{matrix}]$

Problem 27

Find each sum or difference, if possible.

$[\begin{matrix} 6 & - 9 & 2 \\ 4 & 1 & 3 \end{matrix}] + [\begin{matrix} - 8 & 2 & 5 \\ 6 & - 3 & 4 \end{matrix}]$

Problem 29

Find each sum or difference, if possible.

$[\begin{matrix} 2 & 4 & 6 \end{matrix}] + [\begin{matrix} - 2 \\ - 4 \\ - 6 \end{matrix}]$

Problem 35

Find each sum or difference, if possible.

$[\begin{matrix} - 4 & 3 \end{matrix}] - [\begin{matrix} 5 & 8 & 2 \end{matrix}]$

Problem 37

Find each sum or difference, if possible.

$[\begin{matrix} \sqrt{3} & - 4 \\ 2 & - \sqrt{5} \\ - 8 & \sqrt{8} \end{matrix}] - [\begin{matrix} 2 \sqrt{3} & 9 \\ - 2 & \sqrt{5} \\ - 7 & 3 \sqrt{2} \end{matrix}]$

Problem 41

Let $A = [\begin{matrix} - 2 & 4 \\ 0 & 3 \end{matrix}]$ and $B = \left[ \begin{matrix} -6 & 2 \\ 4 & 0 \end{matrix} \right]$ . Find each of the following.

2A

Problem 47

Let $A = [\begin{matrix} - 2 & 4 \\ 0 & 3 \end{matrix}]$ and $B = \left[ \begin{matrix} -6 & 2 \\ 4 & 0 \end{matrix} \right]$ . Find each of the following.

-A + (1/2)B

Problem 55

Find each product, if possible.

$[\begin{matrix} 1 & 2 \\ 3 & 4 \end{matrix}] [\begin{matrix} - 1 \\ 7 \end{matrix}]$

Problem 57

Find each product, if possible.

$[\begin{matrix} 3 & - 4 & 1 \\ 5 & 0 & 2 \end{matrix}] [\begin{matrix} - 1 \\ 4 \\ 2 \end{matrix}]$

Problem 59

Find each product, if possible.

$[\begin{matrix} \sqrt{2} & \sqrt{2} & - \sqrt{18} \\ \sqrt{3} & \sqrt{27} & 0 \end{matrix}] [\begin{matrix} 8 & - 10 \\ 9 & 12 \\ 0 & 2 \end{matrix}]$

Problem 61

Find each product, if possible.

$[\begin{matrix} \sqrt{3} & 1 \\ 2 \sqrt{5} & 3 \sqrt{2} \end{matrix}] [\begin{matrix} \sqrt{3} & - \sqrt{6} \\ 4 \sqrt{3} & 0 \end{matrix}]$

Problem 67

Find each product, if possible.

$[\begin{matrix} - 2 & - 3 & - 4 \\ 2 & - 1 & 0 \\ 4 & - 2 & 3 \end{matrix}] [\begin{matrix} 0 & 1 & 4 \\ 1 & 2 & - 1 \\ 3 & 2 & - 2 \end{matrix}]$

Problem 69

Given $A = [\begin{matrix} 4 & - 2 \\ 3 & 1 \end{matrix}],$ and $C = \left[ \begin{matrix} -5 & 4 & 1 \\ 0 & 3 & 6 \end{matrix} \right]$ , find each product, if possible. See Examples 5–7. BA

Problem 71

Given $A = [\begin{matrix} 4 & - 2 \\ 3 & 1 \end{matrix}],$ , and $C = \left[ \begin{matrix} -5 & 4 & 1 \\ 0 & 3 & 6 \end{matrix} \right]$ , find each product, if possible. See Examples 5–7. BC

Problem 73

Given $A = [\begin{matrix} 4 & - 2 \\ 3 & 1 \end{matrix}],$ , and $C = \left[ \begin{matrix} -5 & 4 & 1 \\ 0 & 3 & 6 \end{matrix} \right]$ , find each product, if possible. See Examples 5–7. AB

Problem 79

For each pair of matrices A and B, find (a) AB and (b) BA. See Example 7. $A = [\begin{matrix} 3 & 4 \\ - 2 & 1 \end{matrix}],$

Problem 80

For each pair of matrices A and B, find (a) AB and (b) BA. $A = [\begin{matrix} 0 & - 5 \\ - 4 & 2 \end{matrix}],$