Lial - College Algebra 13th Edition

Section 5.2

Problem 25

Use the Gauss-Jordan method to solve each system of equations. For systems in two variables with infinitely many solutions, write the solution with y arbitrary. For systems in three variables with infinitely many solutions, write the solution set with z arbitrary.

6x - 3y - 4 = 0

3x + 6y - 7= 0

Problem 27

Use the Gauss-Jordan method to solve each system of equations. For systems in two variables with infinitely many solutions, write the solution with y arbitrary. For systems in three variables with infinitely many solutions, write the solution set with z arbitrary.

2x - y = 6

4x - 2y = 0

Problem 29

Use the Gauss-Jordan method to solve each system of equations. For systems in two variables with infinitely many solutions, write the solution with y arbitrary. For systems in three variables with infinitely many solutions, write the solution set with z arbitrary.

(3/8)x - (1/2)y = 7/8

-6x + 8y = -14

Problem 31

Use the Gauss-Jordan method to solve each system of equations. For systems in two variables with infinitely many solutions, write the solution with y arbitrary. For systems in three variables with infinitely many solutions, write the solution set with z arbitrary.

x + y - 5z = -18

3x - 3y + z = 6

x + 3y - 2z = -13

Section 5.3

Problem 1

What is the value of $∣ \begin{matrix} 4 & 0 \\ - 2 & 0 \end{matrix} ∣$ ?

Problem 3

What expression in x represents $∣ \begin{matrix} x & 4 \\ 3 & x \end{matrix} ∣$ ?

Problem 7

Evaluate each determinant.

$∣ \begin{matrix} - 5 & 9 \\ 4 & - 1 \end{matrix} ∣$

Problem 9

Evaluate each determinant.

$∣ \begin{matrix} - 1 & - 2 \\ 5 & 3 \end{matrix} ∣$

Problem 11

Evaluate each determinant.

$∣ \begin{matrix} 9 & 3 \\ - 3 & - 1 \end{matrix} ∣$

Problem 13

Evaluate each determinant.

$∣ \begin{matrix} 3 & 4 \\ 5 & - 2 \end{matrix} ∣$

Problem 15

Evaluate each determinant.

$∣ \begin{matrix} - 7 & 0 \\ 3 & 0 \end{matrix} ∣$

Problem 17

Find the cofactor of each element in the second row of each matrix.

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

Problem 19

Find the cofactor of each element in the second row of each matrix.

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

Problem 21

Evaluate each determinant.

$∣ \begin{matrix} 4 & - 7 & 8 \\ 2 & 1 & 3 \\ - 6 & 3 & 0 \end{matrix} ∣$

Problem 23

Evaluate each determinant.

$∣ \begin{matrix} 1 & 2 & 0 \\ - 1 & 2 & - 1 \\ 0 & 1 & 4 \end{matrix} ∣$

Problem 25

Evaluate each determinant.

$∣ \begin{matrix} 10 & 2 & 1 \\ - 1 & 4 & 3 \\ - 3 & 8 & 10 \end{matrix} ∣$

Problem 27

Evaluate each determinant.

$∣ \begin{matrix} 1 & - 2 & 3 \\ 0 & 0 & 0 \\ 1 & 10 & - 12 \end{matrix} ∣$

Problem 47

Use the determinant theorems to evaluate each determinant.

$∣ \begin{matrix} 6 & 8 & - 12 \\ - 1 & 0 & 2 \\ 4 & 0 & - 8 \end{matrix} ∣$

Problem 53

Use the determinant theorems to evaluate each determinant.

$∣ \begin{matrix} 1 & 6 & 7 \\ 0 & 6 & 7 \\ 0 & 0 & 9 \end{matrix} ∣$

Problem 57

Use the determinant theorems to evaluate each determinant.

$∣ \begin{matrix} - 1 & 0 & 2 & 3 \\ 5 & 4 & - 3 & 7 \\ 8 & 2 & 9 & - 5 \\ 4 & 4 & - 1 & 10 \end{matrix} ∣$

Problem 59

Use the determinant theorems to evaluate each determinant.

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