Lial - College Algebra 13th Edition

Section 5.7

Problem 81

For each pair of matrices A and B, find (a) AB and (b) BA. $A = [\begin{matrix} 0 & 1 & - 1 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{matrix}],$

Problem 82

For each pair of matrices A and B, find (a) AB and (b) BA.

$A = [\begin{matrix} - 1 & 0 & 1 \\ 0 & 1 & 1 \\ - 1 & - 1 & 0 \end{matrix}],$

Problem 84

Find AB and BA for the following matrices.

$A = [\begin{matrix} a & b \\ c & d \end{matrix}]$

Matrix B acts as the multiplicative element for 2 $\times$ 2 square matrices.

Section 5.8

Problem 1

Answer each question. What is the product of $[\begin{matrix} 6 & 4 \\ - 1 & 8 \end{matrix}]$ and I₂ (in either order)?

Problem 2

Answer each question. What is the product $[\begin{matrix} - 5 & 7 & 4 \\ 2 & 3 & 0 \\ - 1 & 6 & 6 \end{matrix}]$ ?

Problem 9

Are the given matrices inverses of each other? (Hint: Check to see whether their products are the identity matrix I_n.)

$[\begin{matrix} 5 & 7 \\ 2 & 3 \end{matrix}]$

Problem 13

Are the given matrices inverses of each other? (Hint: Check to see whether their products are the identity matrix I_n.)

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

Problem 17

Find the inverse, if it exists, for each matrix. $[\begin{matrix} - 1 & 2 \\ - 2 & - 1 \end{matrix}]$

Problem 19

Find the inverse, if it exists, for each matrix. $[\begin{matrix} - 1 & - 2 \\ 3 & 4 \end{matrix}]$

Problem 21

Find the inverse, if it exists, for each matrix. $[\begin{matrix} 5 & 10 \\ - 3 & - 6 \end{matrix}]$

Problem 23

Find the inverse, if it exists, for each matrix. $[\begin{matrix} 1 & 0 & 1 \\ 0 & - 1 & 0 \\ 2 & 1 & 1 \end{matrix}]$

Problem 25

Find the inverse, if it exists, for each matrix. $[\begin{matrix} 2 & 3 & 3 \\ 1 & 4 & 3 \\ 1 & 3 & 4 \end{matrix}]$

Problem 27

Find the inverse, if it exists, for each matrix. $[\begin{matrix} 2 & 2 & - 4 \\ 2 & 6 & 0 \\ - 3 & - 3 & 5 \end{matrix}]$

Review Exercises

Problem 1

Use the substitution or elimination method to solve each system of equations. Identify any inconsistent systems or systems with infinitely many solutions. If a system has infinitely many solutions, write the solution set with y arbitrary.

2x + 6y = 6

5x + 9y = 9

Problem 8

Use the substitution or elimination method to solve each system of equations. Identify any inconsistent systems or systems with infinitely many solutions. If a system has infinitely many solutions, write the solution set with y arbitrary.

6x + 10y = -11

9x + 6y = -3

Problem 25

Solve each system, using the method indicated.

5x + 2y = -10

3x - 5y = -6 (Gauss-Jordan)

Problem 27

Solve each system, using the method indicated.

3x + y = -7

x - y = -5 (Gaussian elimination)

Problem 29

Solve each system, using the method indicated.

x - z = -3

y + z = 6

2x - 3z = -9 (Gauss-Jordan)

Problem 35

Evaluate each determinant.

$∣ \begin{matrix} - 1 & 8 \\ 2 & 9 \end{matrix} ∣$

Problem 47

Solve each equation. $∣ \begin{matrix} 3 x & 7 \\ - x & 4 \end{matrix} ∣ = 8$

Problem 62

Solve each problem. Find all values of b such that the straight line 3x - y = b touches the circle x² + y² = 25 at only one point.

Problem 64

Solve each problem. Find the equation of the line passing through the points of intersection of the graphs of x² + y² = 20 and x² - y = 0.

Problem 71

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

$[\begin{matrix} 5 & x + 2 \\ - 6 y & z \end{matrix}] = [\begin{matrix} a & 3 x - 1 \\ 5 y & 9 \end{matrix}]$