Deck 7: Systems and Matrices

Question 1

Solve the system graphically.

Answer 1

(4,2),(-4,-2)

Question 2

Solve the system by the elimination method.

Answer 2

(4,-3)

Question 3

Find the solution to the system of equations represented by the augmented matrix.

Answer 3

(5,-2,3)

Question 4

Graph the inequality

Question 5

Solve the system by the substitution method.

Question 6

Write the system of equations as a matrix equation AX=B , with A as the coefficient matrix.

Question 7

When writing the solution to the partial fraction decomposition of what is the first step of this solution?

A)
B)
C)
D)
E)

Question 8

Solve the linear programming problem: Maximize

A) 12
B) 23
C) 25
D) 32

Question 9

There are how many solutions of the system?

A) None
B) One
C) Two
D) Three
E) Four

Question 10

Determine the inequality corresponding to the graph below.

Question 11

Draw a graph representing the solution to the system of inequalities

Question 12

Find the determinant of the matrix

Does matrix B have an inverse?

Question 13

Find the inverse of the matrix

Question 14

A factory records its inventory in matrix X , where column 1 represents Model A of a product, column 2 represents Model B of the same product, and each row represents a color of the product. Matrix M is the price of Model A (row 1) and Model B (row 2). Compute matrix XM and give its physical interpretation.

Question 15

Use an inverse matrix to solve the system given in Problem 1 .

Question 16

Write the partial fraction decomposition of

Question 17

The system below has an infinite number of solutions. Find the solution set.

Question 18

Using matrix and

which of the following is a true
statement?

A) Matrix A has an inverse.
B)
C) AB exists and BA does not exist.
D) BA exists and AB does not exist.

Question 19

Show that matrix
is the inverse
of the matrix

Question 20

Find the determinant of the matrix

Question 21

Solve the system by elimination.

Question 22

Question 23

Question 24

Write the system of equations for the augmented matrix. Do not solve.

Question 25

Solve the system graphically. Round answers to the nearest hundredth.

Question 26

Tell what elementary row operation can be applied to
to obtain

A)
B)
C)
D)

Question 27

Find of the matrix

Question 28

Use Gaussian elimination to solve the system.

Question 29

A company's inventory for two models of computers and two models of palm-pilots is given by the matrix
where row 1 represents the computers, row 2 represents the palm-pilots, column 1 represents Model A, and column 2 represents Model B. If the company wants to increase inventory by 15% in the next month, what will be the projected matrix for the inventory? Use matrices and explain.

Question 30

Use Gaussian elimination to solve the system.

Question 31

Use Gaussian elimination to solve the system.

Question 32

Determine the number of solutions to the augmented matrix.

A) infinitely many
B) 2 solutions
C) 1 solution
D) no solutions

Question 33

Solve the system graphically. Round answers to the nearest hundredth.

Question 34

Solve the linear programming problem. Maximize C=-3x+5y subject to:

Question 35

Solve the system by substitution.

Question 36

Solve the system by elimination.

Question 37

The inverse of matrix
Solve the following system by the method of inverse matrix.

Question 38

Tell what elementary row operation can be applied to

to obtain

A)
B)
C)
D)

Question 39

Solve the system by substitution.

Question 40

What is the partial fraction decomposition of

Question 41

Question 42

The inverse of matrix

Solve the following system by the method of inverse matrix.

Question 43

What is the partial fraction decomposition of

Question 44

Determine the number of solutions to the augmented matrix.

A) infinitely many
B) 2 solutions
C) 1 solution
D) no solutions

Question 45

A company's inventory for two models of televisions and two models of radios is given by the matrix

, where row 1 represents the televisions, row 2 represents the radios, column 1 represents Model A, and column 2 represents Model B. If the company wants to increase inventory by 20% in the next month, what will be the projected matrix for the inventory? Use matrices and explain.

Question 46

Write the system of equations for the augmented matrix. Do not solve.

Question 47

Use Gaussian elimination to solve the system.

Question 48

Solve the linear programming problem. Maximize subject to:

Question 49

Find of the matrix

Question 50

Connor invested a total of $ 50,000 in three different investments that yield 5%, 7% , and 10% per year, respectively. The total income per year from the three investments is $ 3,764 . If the income from the 7% investment is half the income of the 10% investment, what amount did Jose invest in each investment?
(a) Write the system of equations that will solve this problem. Do not solve.
(b) Write the system as a matrix equation A X=B . Do not solve.