Lial - College Algebra 13th Edition

Ch. 5 - Systems and Matrices

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Lial 13th Edition

Ch. 5 - Systems and Matrices

Section 5.1

Problem 7

Solve each system by substitution.

4x + 3y = -13

-x + y = 5

Problem 9

Solve each system by substitution.

x - 5y = 8

x = 6y

Problem 11

Solve each system by substitution.

8x - 10y = -22

3x + y = 6

Problem 13

Solve each system by substitution.

7x - y = -10

3y - x = 10

Problem 15

Solve each system by substitution.

-2x = 6y + 18

-29 = 5y - 3x

Problem 17

Solve each system by substitution.

3y = 5x + 6

x + y = 2

Problem 19

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

4x + y = -23

x - 2y = -17

Problem 21

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

2x - 3y = -7

5x + 4y = 17

Problem 23

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

5x + 7y = 6

10x - 3y = 46

Problem 25

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

6x + 7y + 2 = 0

7x - 6y - 26 = 0

Problem 27

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

x/2+ y/3 = 4

3x/2+3y/2 = 15

Problem 29

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

(2x-1)/3 + (y+2)/4 = 4

(x+3)/2 - (x-y)/2 = 3

Problem 31

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.

9x - 5y = 1

-18x + 10y = 1

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 69

Solve each system. (Hint: In Exercises 69–72, let 1/x = t and 1/y = u.)

2/x + 1/y = 3/2

3/x - 1/y = 1

Problem 75

For what value(s) of k will the following system of linear equations have no solution? infinitely many solutions?

x - 2y = 3

-2x + 4y = k

Problem 77

Use a system of equations to solve each problem. See Example 8. Find an equation of the line y = ax + b that passes through the points (-2, 1) and (-1, -2).

Problem 79

Use a system of equations to solve each problem. Find an equation of the parabola y = ax² + bx + c that passes through the points (2, 3), (-1, 0), and (-2, 2).

Section 5.2

Problem 1

How many rows and how many columns does this matrix have? What is its dimension?

$[\begin{matrix} - 2 & 5 & 8 & 0 \\ 1 & 13 & - 6 & 9 \end{matrix}]$

Problem 3

What is the augmented matrix of the following system?

-3x + 5y = 2

6x + 2y = 7

Problem 7

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

$[\begin{matrix} 1 & 4 \\ 4 & 7 \end{matrix}],$

Problem 8

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

$[\begin{matrix} 1 & - 4 \\ 7 & 0 \end{matrix}],$

Problem 9

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

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

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 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 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 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 19

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

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 23

3x + 2y = -9

2x - 5y = -6