Lial - College Algebra 13th Edition

Ch. 5 - Systems and Matrices

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Lial 13th Edition

Ch. 5 - Systems and Matrices

Problem 9

Are the given matrices inverses of each other? (Hint: Check to see whether their products are the identity matrix I_n.)

$[\begin{matrix} 5 & 7 \\ 2 & 3 \end{matrix}]$

Problem 9

Find the dimension of each matrix. Identify any square, column, or row matrices.

$[\begin{matrix} - 6 & 8 & 0 & 0 \\ 4 & 1 & 9 & 2 \\ 3 & - 5 & 7 & 1 \end{matrix}]$

Problem 9

Evaluate each determinant.

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

Problem 10

Use the given row transformation to change each matrix as indicated.

$[\begin{matrix} 1 & 5 & 6 \\ - 4 & - 1 & 2 \\ 3 & 7 & 1 \end{matrix}],$

Problem 10

Find the dimension of each matrix. Identify any square, column, or row matrices.

$[\begin{matrix} 8 & - 2 & 4 & 6 & 3 \end{matrix}]$

Problem 11

Find the dimension of each matrix. Identify any square, column, or row matrices.

$[\begin{matrix} 2 \\ 4 \end{matrix}]$

Problem 11

Solve each system by substitution.

8x - 10y = -22

3x + y = 6

Problem 11

Evaluate each determinant.

$∣ \begin{matrix} 9 & 3 \\ - 3 & - 1 \end{matrix} ∣$

Problem 11

Verify that the points of intersection specified on the graph of each nonlinear system are solutions of the system by substituting directly into both equations.

y = 3x²

x² + y² = 10

Problem 11

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

Problem 11

Graph each inequality. x + 2y ≤ 6

Problem 12

Find the dimension of each matrix. Identify any square, column, or row matrices. See the discussion preceding Example 1.

$∣ \begin{matrix} - 9 \end{matrix} ∣$

Problem 13

Write the augmented matrix for each system and give its dimension. Do not solve.

2x + y + z - 3 = 0

3x - 4y + 2z + 7 = 0

x + y + z - 2 = 0

Problem 13

Are the given matrices inverses of each other? (Hint: Check to see whether their products are the identity matrix I_n.)

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

Problem 13

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

Problem 13

Solve each system by substitution.

7x - y = -10

3y - x = 10

Problem 13

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

$[\begin{matrix} - 3 & a \\ b & 5 \end{matrix}] = [\begin{matrix} c & 0 \\ 4 & d \end{matrix}]$

Problem 13

Evaluate each determinant.

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

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.

-2x = 6y + 18

-29 = 5y - 3x

Problem 15

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

x² - y = 0

x + y = 2

Problem 15

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

$[\begin{matrix} 3 & 2 & 1 & 1 \\ 0 & 2 & 4 & 22 \\ - 1 & - 2 & 3 & 15 \end{matrix}]$

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 15

Evaluate each determinant.

$∣ \begin{matrix} - 7 & 0 \\ 3 & 0 \end{matrix} ∣$

Problem 15

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

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

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

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

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

Problem 17

Find the cofactor of each element in the second row of each matrix.

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