Lial - College Algebra 13th Edition

Ch. 5 - Systems and Matrices

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Lial 13th Edition

Ch. 5 - Systems and Matrices

Problem 23

Evaluate each determinant. See Example 3.

Problem 23

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. See Examples 1-4. 3x + 2y = -9 2x - 5y = -6

Problem 24

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

$x^{2} + y^{2} = 102$

$x^{2} - y^{2} = 17$

Problem 25

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

Problem 25

Solve each system by elimination. In systems with fractions, first clear denominators. See Example 2. 6x + 7y + 2 = 0 7x - 6y - 26 = 0

Problem 25

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

Problem 25

Evaluate each determinant. See Example 3.

Problem 25

Solve each system, using the method indicated. 5x + 2y = -10 3x - 5y = -6 (Gauss-Jordan)

Problem 25

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

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 27

Problem 28

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

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 29

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

Problem 29

Solve each system by elimination. In systems with fractions, first clear denominators. See Example 2. (2x-1)/3 + (y+2)/4 = 4 (x+3)/2 - (x-y)/2 = 3

Problem 29

Solve each system, using the method indicated. x - z = -3 y + z = 6 2x - 3z = -9 (Gauss-Jordan)

Problem 29

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

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

Problem 33

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

Problem 34

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

$5 x^{2} - 2 y^{2} = 25$

$10 x^{2} + y^{2} = 50$