Lial - College Algebra 13th Edition

Ch. 5 - Systems and Matrices

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Lial 13th Edition

Ch. 5 - Systems and Matrices

Problem 34

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

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

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

Problem 35

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.

5x - 5y - 3 = 0

x - y - 12 = 0

Problem 35

Find each sum or difference, if possible.

$[\begin{matrix} - 4 & 3 \end{matrix}] - [\begin{matrix} 5 & 8 & 2 \end{matrix}]$

Problem 35

Evaluate each determinant.

$∣ \begin{matrix} - 1 & 8 \\ 2 & 9 \end{matrix} ∣$

Problem 35

Match each inequality with the appropriate calculator graph in A–D. Do not use a calculator y ≤ -3x - 6

Problem 37

Evaluate each determinant.

$∣ \begin{matrix} x & 4 x \\ 2 x & 8 x \end{matrix} ∣$

Problem 37

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

2xy + 1 = 0

x + 16y = 2

Problem 37

Find the partial fraction decomposition for each rational expression. See Examples 1–4. (x²)/(x⁴ - 1)

Problem 37

Graph the solution set of each system of inequalities.

x + y ≥ 0

2x - y ≥ 3

Problem 37

Find each sum or difference, if possible.

$[\begin{matrix} \sqrt{3} & - 4 \\ 2 & - \sqrt{5} \\ - 8 & \sqrt{8} \end{matrix}] - [\begin{matrix} 2 \sqrt{3} & 9 \\ - 2 & \sqrt{5} \\ - 7 & 3 \sqrt{2} \end{matrix}]$

Problem 39

Graph the solution set of each system of inequalities.

2x + y > 2

x - 3y < 6

Problem 39

Evaluate each determinant.

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

Problem 39

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

3x² - y² = 11

xy = 12

Problem 39

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

Problem 40

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

Problem 41

Determine the system of equations illustrated in each graph. Write equations in standard form.

Problem 41

Let $A = [\begin{matrix} - 2 & 4 \\ 0 & 3 \end{matrix}]$ and $B = \left[ \begin{matrix} -6 & 2 \\ 4 & 0 \end{matrix} \right]$ . Find each of the following.

Problem 41

Graph the solution set of each system of inequalities.

3x + 5y ≤ 15

x² + y² < 9

Problem 42

Determine the system of equations illustrated in each graph. Write equations in standard form.

Problem 43

Graph the solution set of each system of inequalities.

4x - 3y ≤ 12

y ≤ x²

Problem 43

Let and . Find each of the following. See Examples 2 –4.

(3/2)B

Problem 45

Graph the solution set of each system of inequalities. x + 2y ≤ 4 y ≥ x² - 1

Problem 46

Let and . Find each of the following. See Examples 2 –4.

2A + 4B

Problem 47

Let $A = [\begin{matrix} - 2 & 4 \\ 0 & 3 \end{matrix}]$ and $B = \left[ \begin{matrix} -6 & 2 \\ 4 & 0 \end{matrix} \right]$ . Find each of the following.

-A + (1/2)B

Problem 47

Use the determinant theorems to evaluate each determinant.

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

Problem 47

Solve each equation. $∣ \begin{matrix} 3 x & 7 \\ - x & 4 \end{matrix} ∣ = 8$

Problem 48

Solve each equation.

Problem 48

Graph the solution set of each system of inequalities.

y ≥ (x - 2)² + 3

y ≤ -(x - 1)² + 6

Problem 49

Use the determinant theorems to evaluate each determinant. See Example 4.

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

Problem 51

Graph the solution set of each system of inequalities.

y ≥ x² + 4x + 4

y < -x²