Lial - College Algebra 13th Edition

Ch. 5 - Systems and Matrices

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Lial 13th Edition

Ch. 5 - Systems and Matrices

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 51

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

Problem 52

Graph the solution set of each system of inequalities.

$y>x^2+2$

$y\le x-2$

Problem 53

Graph the solution set of each system of inequalities.

$3 x minus 2 y is greater than or equal to 6$

$x + y \leq - 5$

$y is less than or equal to 4$

Problem 53

Use the determinant theorems to evaluate each determinant.

$∣ \begin{matrix} 1 & 6 & 7 \\ 0 & 6 & 7 \\ 0 & 0 & 9 \end{matrix} ∣$

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 55

Solve each problem using a system of equations in two variables. See Example 6. Find two numbers whose sum is 17 and whose product is 42.

Problem 55

Find each product, if possible.

$[\begin{matrix} 1 & 2 \\ 3 & 4 \end{matrix}] [\begin{matrix} - 1 \\ 7 \end{matrix}]$

Problem 57

Solve each problem using a system of equations in two variables. See Example 6. Find two numbers whose squares have a sum of 100 and a difference of 28.

Problem 57

Graph the solution set of each system of inequalities.

$x is less than or equal to 4$

$x is greater than or equal to 0$

$y is greater than or equal to 0$

$x plus 2 y is greater than or equal to 2$

Problem 57

Find each product, if possible.

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

Problem 57

Use the determinant theorems to evaluate each determinant.

$∣ \begin{matrix} - 1 & 0 & 2 & 3 \\ 5 & 4 & - 3 & 7 \\ 8 & 2 & 9 & - 5 \\ 4 & 4 & - 1 & 10 \end{matrix} ∣$

Problem 58

Graph the solution set of each system of inequalities.

$2y+x\ge-5$

$y\le3+x$

$x\le0$

$y\le0$

Problem 59

Use the determinant theorems to evaluate each determinant.

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

Problem 59

Graph the solution set of each system of inequalities.

$2 x plus 3 y is less than or equal to 12$

$2 x + 3 y > - 6$

$3 x plus y is less than 4$

$x is greater than or equal to 0$

$y is greater than or equal to 0$

Problem 59

Solve each problem using a system of equations in two variables. See Example 6. Find two numbers whose ratio is 9 to 2 and whose product is 162.

Problem 59

Find each product, if possible.

$[\begin{matrix} \sqrt{2} & \sqrt{2} & - \sqrt{18} \\ \sqrt{3} & \sqrt{27} & 0 \end{matrix}] [\begin{matrix} 8 & - 10 \\ 9 & 12 \\ 0 & 2 \end{matrix}]$

Problem 60

Solve each problem using a system of equations in two variables. See Example 6. Find two numbers whose ratio is 4 to 3 and are such that the sum of their squares is 100.

Problem 61

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

$∣ \begin{matrix} 3 & - 6 & 5 & - 1 \\ 0 & 2 & - 1 & 3 \\ - 6 & 4 & 2 & 0 \\ - 7 & 3 & 1 & 1 \end{matrix} ∣$

Problem 61

Find each product, if possible.

$[\begin{matrix} \sqrt{3} & 1 \\ 2 \sqrt{5} & 3 \sqrt{2} \end{matrix}] [\begin{matrix} \sqrt{3} & - \sqrt{6} \\ 4 \sqrt{3} & 0 \end{matrix}]$

Problem 61

Solve each problem using a system of equations in two variables. See Example 6. The longest side of a right triangle is 13 m in length. One of the other sides is 7 m longer than the shortest side. Find the lengths of the two shorter sides of the triangle.

Problem 62

Solve each problem. Find all values of b such that the straight line 3x - y = b touches the circle x² + y² = 25 at only one point.

Problem 62

Graph the solution set of each system of inequalities.

$y\le x^3-x$

$y>-3$

Problem 63

Answer each question. Does the straight line 3x - 2y = 9 intersect the circle x² + y² = 25? (Hint: To find out, solve the system formed by these two equations.)

Problem 63

Use Cramer's rule to solve each system of equations. If D = 0, then use another method to determine the solution set. See Examples 5–7.

x + y = 4

2x - y = 2

Problem 63

Find each product, if possible. See Examples 5–7. <4x2 Matrix>

Problem 64

Solve each problem. Find the equation of the line passing through the points of intersection of the graphs of x² + y² = 20 and x² - y = 0.

Problem 64

Graph the solution set of each system of inequalities.

$y\ge3^{x}$

$y\ge2$

Problem 65

Answer each question. A line passes through the points of intersection of the graphs of y = x² and x² + y² = 90. What is the equation of this line?

Problem 65

Graph the solution set of each system of inequalities.

$y \leq \log x$

$y \geq ∣ x - 2 ∣$