Lial - College Algebra 13th Edition

Ch. 5 - Systems and Matrices

Back

All textbooks

Lial 13th Edition

Ch. 5 - Systems and Matrices

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 79

Perform each operation, if possible.

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

Problem 79

Find the maximum and minimum values of each objective function over the region of feasible solutions shown at the right. objective function = 3x + 5y

Problem 80

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

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 81

Find the maximum and minimum values of each objective function over the region of feasible solutions shown at the right. objective function = 10y

Problem 81

Perform each operation, if possible.

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

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 83

Find the inverse, if it exists, for each matrix.

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

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.

Problem 85

Find the inverse, if it exists, for each matrix.

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

Problem 99

Solve each problem. See Examples 5 and 9. The sum of two numbers is 47, and the difference between the numbers is 1. Find the numbers.

Problem 100

Solve each problem. See Examples 5 and 9. At the Berger ranch, 6 goats and 5 sheep sell for $305, while 2 goats and 9 sheep sell for $285. Find the cost of a single goat and of a single sheep.

Problem 102

Solve each problem. See Examples 5 and 9. A cashier has a total of 30 bills, made up of ones, fives, and twenties. The number of twenties is 9 more than the number of ones. The total value of the money is $351. How many of each denomination of bill are there?

Problem 106

Solve each problem. See Examples 5 and 9. The sum of the measures of the angles of any triangle is 180°. In a certain triangle, the largest angle measures 55° less than twice the medium angle, and the smallest angle measures 25° less than the medium angle. Find the measures of all three angles.

Problem 109

Solve each problem. See Examples 5 and 9. Solve the system of equations (4), (5), and (6) from Example 9.

$25 x + 40 y + 20 z = 2200$ (4)

$4 x + 2 y + 3 z = 280$ (5)

$3 x + 2 y + z = 180$ (6)