Lial - College Algebra 13th Edition

Ch. 5 - Systems and Matrices

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Lial 13th Edition

Ch. 5 - Systems and Matrices

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 17

Solve each system by substitution.

3y = 5x + 6

x + y = 2

Problem 17

Solve each nonlinear system of equations. Give all solutions, including those with nonreal complex components.

y = x² - 2x + 1

x - 3y = -1

Problem 17

Find the values of the variables for which each statement is true, if possible.

$[\begin{matrix} x & y & z \end{matrix}] = [\begin{matrix} 21 & 6 \end{matrix}]$

Problem 17

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

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 18

Graph each inequality. 2x > 3 - 4y

Problem 19

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

Problem 19

Find the inverse, if it exists, for each matrix. $[\begin{matrix} - 1 & - 2 \\ 3 & 4 \end{matrix}]$

Problem 19

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

4x + y = -23

x - 2y = -17

Problem 19

Find the values of the variables for which each statement is true, if possible.

$[\begin{matrix} 0 & 5 & x \\ - 1 & 3 & y + 2 \\ 4 & 1 & z \end{matrix}] = [\begin{matrix} 0 & w & 6 \\ - 1 & 3 & 0 \\ 4 & 1 & 8 \end{matrix}]$

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.

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

Problem 19

Graph each inequality. x ≤ 3

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

Find the values of the variables for which each statement is true, if possible.

$[\begin{matrix} - 7 + z & 4 r & 8 s \\ 6 p & 2 & 5 \end{matrix}] + [\begin{matrix} - 9 & 8 r & 3 \\ 2 & 5 & 4 \end{matrix}] = [\begin{matrix} 2 & 36 & 27 \\ 20 & 7 & 12 a \end{matrix}]$

Problem 21

Graph each inequality. y < 3x² + 2

Problem 21

Find the inverse, if it exists, for each matrix. $[\begin{matrix} 5 & 10 \\ - 3 & - 6 \end{matrix}]$

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.

x + y = 5

x - y = -1

Problem 21

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

2x - 3y = -7

5x + 4y = 17

Problem 21

Evaluate each determinant.

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

Problem 21

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

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

3x + 2y = -9

2x - 5y = -6

Problem 23

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

Problem 23

Evaluate each determinant.

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

Problem 23

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

5x + 7y = 6

10x - 3y = 46

Problem 23

Find the inverse, if it exists, for each matrix. $[\begin{matrix} 1 & 0 & 1 \\ 0 & - 1 & 0 \\ 2 & 1 & 1 \end{matrix}]$

Problem 24

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

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

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