Lial - College Algebra 13th Edition

Ch. 5 - Systems and Matrices

Back

All textbooks

Lial 13th Edition

Ch. 5 - Systems and Matrices

Problem 25

Solve each system, using the method indicated.

5x + 2y = -10

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

Problem 25

Graph each inequality. x² + (y + 3)² ≤ 16

Problem 25

Find the partial fraction decomposition for each rational expression. See Examples 1–4. (3x - 2)/((x + 4)(3x² + 1))

Problem 25

Solve each system by elimination. In systems with fractions, first clear denominators.

6x + 7y + 2 = 0

7x - 6y - 26 = 0

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 25

Evaluate each determinant.

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

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 26

Solve each nonlinear system of equations. Give all solutions, including those with nonreal complex components. See Examples 1–5.

$x^{2} + y^{2} = 02$

$x^{2} - 3 y^{2} = 0$

Problem 27

Evaluate each determinant.

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

Problem 27

Solve each system by elimination. In systems with fractions, first clear denominators.

x/2+ y/3 = 4

3x/2+3y/2 = 15

Problem 27

Solve each system, using the method indicated.

3x + y = -7

x - y = -5 (Gaussian elimination)

Problem 27

2x - y = 6

4x - 2y = 0

Problem 27

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

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 27

Graph each inequality. y > 2^x + 1

Problem 27

Find the partial fraction decomposition for each rational expression. See Examples 1–4. 1/(x(2x + 1)(3x² + 4))

Problem 28

Solve each nonlinear system of equations. Give all solutions, including those with nonreal complex components. See Examples 1–5.

$x^{2} + 2 y^{2} = 9$

$x^{2} + y^{2} = 25$

Problem 28

Graph each inequality. y ≤ log(x - 1) - 2

Problem 29

Solve each system by elimination. In systems with fractions, first clear denominators.

(2x-1)/3 + (y+2)/4 = 4

(x+3)/2 - (x-y)/2 = 3

Problem 29

Find each sum or difference, if possible.

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

Problem 29

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

-6x + 8y = -14

Problem 29

Solve each system, using the method indicated.

x - z = -3

y + z = 6

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

Problem 29

Find the partial fraction decomposition for each rational expression. See Examples 1–4. (2x⁵ + 3x⁴ - 3x³ - 2x² + x)/(2x² + 5x + 2)

Problem 30

Solve each nonlinear system of equations. Give all solutions, including those with nonreal complex components. See Examples 1–5.

$3 x^{2} + 5 y^{2} = 17$

$2 x^{2} - 3 y^{2} = 5$

Problem 31

x + y - 5z = -18

3x - 3y + z = 6

x + 3y - 2z = -13

Problem 31

Solve each system of equations. State whether it is an inconsistent system or has infinitely many solutions. If a system has infinitely many solutions, write the solution set with x arbitrary.

9x - 5y = 1

-18x + 10y = 1

Problem 31

Find the partial fraction decomposition for each rational expression. See Examples 1–4. (3x - 1)/(x(2x² + 1)²)

Problem 32

Work each problem. Write the inequality that represents the region inside a circle with center (-5, -2) and radius 4.

Problem 33

Find each sum or difference, if possible. See Examples 2 and 3.

Problem 33

Find the partial fraction decomposition for each rational expression. See Examples 1–4. (-x⁴ - 8x² + 3x - 10)/((x + 2)(x² + 4)²)