Lial - College Algebra 13th Edition - Chapter 6

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Ch. 5 - Systems and Matrices

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Lial 13th Edition

Ch. 5 - Systems and Matrices

Problem 13

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

Problem 14

Write the augmented matrix for each system and give its dimension. Do not solve. 4x - 2y + 3z - 4 = 0 3x + 5y + z - 7 = 0 5x - y + 4z - 7 = 0

Problem 14

Graph each inequality. 4y - 3x ≤ 5

Problem 15

Solve each system by substitution. See Example 1. -2x = 6y + 18 -29 = 5y - 3x

Problem 15

Evaluate each determinant. See Example 1.

Problem 15

Write the system of equations associated with each augmented matrix . Do not solve. <4x3 Matrix>

Problem 15

Find the partial fraction decomposition for each rational expression. See Examples 1–4. (4x^2 - x - 15)/(x(x + 1)(x - 1))

Problem 16

Graph each inequality. x < 3 + 2y

Problem 16

Solve each problem using a system of equations. A company sells recordable CDs for $0.80 each and play-only CDs for $0.60 each. The company receives $76.00 for an order of 100 CDs. However, the customer neglected to specify how many of each type to send. Determine the number of each type of CD that should be sent.

Problem 17

Solve each system by substitution. See Example 1. 3y = 5x + 6 x + y = 2

Problem 17

Find the cofactor of each element in the second row of each matrix. See Example 2.

Problem 17

Write the system of equations associated with each augmented matrix . Do not solve. <4x3 Matrix>

Problem 17

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

Problem 18

Graph each inequality. 2x > 3 - 4y

Problem 18

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

$y = x^{2} + 6 x + 9$

$x + 2 y = - 2$

Problem 19

Graph each inequality. x ≤ 3

Problem 19

Solve each system by elimination. In systems with fractions, first clear denominators. See Example 2. 4x + y = -23 x - 2y = -17

Problem 19

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

Problem 19

Find the cofactor of each element in the second row of each matrix. See Example 2.

Problem 19

Find the values of the variables for which each statement is true, if possible. See Examples 1 and 2. =

Problem 19

Write the system of equations associated with each augmented matrix . Do not solve.

Problem 20

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

$y = 6 x + x^{2}$

$4 x - y = - 3$

Problem 21

Graph each inequality. y < 3x² + 2

Problem 21

Find the partial fraction decomposition for each rational expression. See Examples 1–4. (x³ + 4)/(9x³ - 4x)

Problem 21

Evaluate each determinant. See Example 3.

Problem 21

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. x + y = 5 x - y = -1

Problem 22

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

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

$- 3 x + 4 y = 2$

Problem 23

Graph each inequality. y > (x - 1)² + 2

Problem 23

Solve each system by elimination. In systems with fractions, first clear denominators. See Example 2. 5x + 7y = 6 10x - 3y = 46

Problem 23

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