Free Printable Chapter 6: Systems of Linear Equations and Matrices

1.

Solve the system of equations using Gaussian Elimination.

25x + 60y + 80z = 510

40x + 20y + 15z = 325

60x + 90y + 100z = 840

a)

(6, 2, 3)

b)

(3, 2, 6)

c)

(6, 3, 2)

d)

(3, 6, 2)

2.

Solve the system of linear equations.

4x + 3y – z = –10

–2x – y + 5z = 24

–3x + 2y – 6z = –11

a)

x = –3, y = 2, z = 4

b)

x = –2, y = 2, z = 4

c)

x = 2, y = 2, z = 4

d)

x = 3, y = 2, z = 4 x = 3, y = 2, z = 4

3.

Write the augmented matrix for the system of linear equations.

2w – 3x + 4z = –12

–3w + 6y – 9z = 7

–x + 4y – 5z = 2

w + 6x + 4y = –9

a)

b)

c)

d)

4.

Which of the following matrices is in row-echelon form?

a)

b)

c)

d)

5.

Find the inverse of

a)

b)

c)

d)

6.

Which of the following shows the system of equations using a matrix equation?

a)

b)

c)

d)

7.

Solve the systems of equations by using matrix equations.

a)

b)

c)

d)

8.

Find the value of the determinant.

a)

-29

b)

-3

c)

-43

d)

-25

9.

Use an inverse matrix to solve the system of equations.

7x − 9y = 13

−4x + 5y = −8

a)

x = -7, y = -4

b)

x = 7, y = 4

c)

x = -123, y = 157

d)

x = 123, y = -157

10.

Bonny has 21 coins consisting of quarters, dimes, and nickels. The total value of the coins is $4.05. She has twice as many quarters as dimes and nickels combined. Write a system of equations that represent the situation.

a)

b)

c)

d)

11.

Bonny has 21 coins consisting of quarters, dimes, and nickels. The total value of the coins is $4.05. (work in dollars, not cents) She has twice as many quarters as dimes and nickels combined. Find the inverse matrix for the system of equations.

a)

b)

c)

d)

12.

Bonny has 21 coins consisting of quarters, dimes, and nickels. The total value of the coins is $4.05. She has twice as many quarters as dimes and nickels combined. How many of each coin does Bonny have?

a)

14 quarters, 4 dimes, 3 nickels

b)

22 quarters, 7 dimes, 4 nickels

c)

12 quarters, 4 dimes, 2 nickels

d)

16 quarters, 5 dimes, 3 nickels

13.

Decompose\ \frac{12}{x^2-4}\ into\ partial\ fractions.

a)

$\frac{3}{x+2}-\frac{3}{x-2}$

b)

$\frac{3}{x-2}-\frac{3}{x+2}$

c)

$\frac{3}{x-2}+\frac{3}{x+2}$

d)

$\frac{3}{x+2}+\frac{3}{2x+1}$

14.

Find\ the\ partial\ fraction\ decomposition\ of\ \frac{x+23}{x^2-4x-21}

a)

$-\frac{2}{x+7}+\frac{3}{x-3}$

b)

$\frac{3}{x+7}+\frac{-2}{x-3}$

c)

$\frac{-2}{x-7}+\frac{3}{x+3}$

d)

$\frac{3}{x-7}+\frac{-2}{x+3}$

15.

Which of the following is the partial fraction decomposition of

$\frac{-14x+42}{x^2-4x-45}$

a)

$\frac{-8}{x+5}-\frac{6}{x-9}$

b)

$\frac{-2}{x-5}+\frac{-12}{x+9}$

c)

$\frac{6}{x+5}+\frac{-8}{x-9}$

d)

$\frac{-12}{x-5}+\frac{-2}{x+9}$

16.

Find the partial fraction decomposition of

$\frac{-2x^3+6x^2+9x-15}{x^2-3x}$

a)

$-2x+\frac{-5}{x}+\frac{14}{x-3}$

b)

$-2x+\frac{4}{x}+\frac{5}{x-3}$

c)

$-2x+\frac{5}{x}+\frac{4}{x-3}$

d)

$-2x+\frac{-5}{x}+\frac{-14}{x-3}$

17.

Suppose a lumber mill can turn out up to 900 units of product each week. The mill must produce at least 100 units of lumber and 400 units of plywood. Write the constraints as a system of inequalities where x = the number of units of lumber and y = the number of units of plywood.

a)

$x\le100,\ y\ge400,\ and\ x+y\ \ge900$

b)

$x\ge100,\ y\ge400,\ and\ x+y\le900$

c)

$x\ge100,\ y\le400,\ and\ x+y\ge900$

d)

$x\ge100,\ y\le400,\ and\ x+y\le900$

18.

What are the vertices of the triangle formed?

a)

(100, 400), (400, 500), and (100, 800)

b)

(100, 400), (500, 400), and (800, 100)

c)

(100, 400), (400, 500), and (800, 100)

d)

(100, 400), (500, 400), and (100, 800)

19.

The profit for each unit of lumber is $40 and the profit for each unit of plywood is $60. Write a profit function P(x, y) if x = the number of units of lumber and y = the number of units of plywood.

a)

P(x, y) = 60x + 40y

b)

P(x, y) = 40x + 60y

c)

P(x, y) = 60x - 40y

d)

P(x, y) = 40x - 60y

20.

Use the function P(x, y) = 40x + 60y to determine how many of each item should be produced in order to maximize profit.

a)

(100, 400)

b)

(100, 800)

c)

(500, 400)

d)

(300, 500)

Chapter 6: Systems of Linear Equations and Matrices

Total questions: 20

Worksheet time: 40mins

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