Lial - College Algebra 13th Edition

Ch. 5 - Systems and Matrices

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Lial 13th Edition

Ch. 5 - Systems and Matrices

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. See Examples 3 and 4. 5x - 5y - 3 = 0 x - y - 12 = 0

Problem 35

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

Problem 35

Evaluate each determinant.

Problem 37

Graph the solution set of each system of inequalities. x + y ≥ 0 2x - y ≥ 3

Problem 37

Evaluate each determinant.

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

Problem 37

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

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

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

Graph the solution set of each system of inequalities. 3x + 5y ≤ 15 x^2 + y^2 < 9

Problem 41

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

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

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

Problem 47

Solve each equation. = 8

Problem 48

Graph the solution set of each system of inequalities. y ≥ (x - 2)² + 3 y ≤ -(x - 1)² + 6

Problem 48

Solve each equation.

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

Problem 51

Find the partial fraction decomposition for each rational expression. 5-2x / (x² + 2)(x - 1)

Problem 51

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

$∣ \begin{matrix} 0 & 1 & - 3 \\ 7 & 5 & 2 \\ 1 & - 2 & 6 \end{matrix} ∣$

Problem 52

Graph the solution set of each system of inequalities.

$y>x^2+2$

$y\le x-2$

Problem 53

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

Problem 53

Graph the solution set of each system of inequalities.

$3x-2y\ge6$

$x+y\le-5$

$y\le4$

Problem 55

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

$∣ \begin{matrix} 2 & - 1 & 3 \\ 6 & 4 & 10 \\ 4 & 5 & 7 \end{matrix} ∣$

Problem 57

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