Algebra 2

Holliday, Luchin, Cuevas, Carter Marks, Day, Casey, Hayek

Chapter 4

Matrices - all with Video Answers

Educators

Section 1

Introduction to Matrices

Problem 1

WEATHER For Exercises 1 and $2,$ use the table that shows a five-day forecast indicating high (H) and low (L) temperatures.
Organize the temperatures in a matrix.

Grant Westfall

Grant Westfall

Numerade Educator

Problem 2

WEATHER For Exercises 1 and $2,$ use the table that shows a five-day forecast indicating high (H) and low (L) temperatures.
Which day will be the warmest?

Grant Westfall

Numerade Educator

Problem 3

State the dimensions of each matrix.
$$
\left[\begin{array}{lllll}{3} & {4} & {5} & {6} & {7}\end{array}\right]
$$

Grant Westfall

Numerade Educator

Problem 4

State the dimensions of each matrix.
$$
\left[\begin{array}{rrrr}{10} & {-6} & {18} & {0} \\ {-7} & {5} & {2} & {4} \\ {3} & {11} & {9} & {7}\end{array}\right]
$$

Grant Westfall

Numerade Educator

Problem 5

Solve each equation.
$$
\left[\begin{array}{c}{x+4} \\ {2 y}\end{array}\right]=\left[\begin{array}{c}{9} \\ {12}\end{array}\right]
$$

Grant Westfall

Numerade Educator

Problem 6

Solve each equation.
$$
[9 \quad 13]=[x+2 y \quad 4 x+1]
$$

Grant Westfall

Numerade Educator

Problem 7

Organize the information in a matrix.
(PICTURE NOT COPY)

Charles Carter

Numerade Educator

Problem 8

Organize the information in a matrix.
(PICTURE NOT COPY)

Charles Carter

Numerade Educator

Problem 9

State the dimensions of each matrix.
$$
\left[\begin{array}{rrr}{6} & {-1} & {5} \\ {-2} & {3} & {-4}\end{array}\right]
$$

Grant Westfall

Numerade Educator

Problem 10

State the dimensions of each matrix.
$$
\left[\begin{array}{l}{7} \\ {8} \\ {9}\end{array}\right]
$$

Grant Westfall

Numerade Educator

Problem 11

State the dimensions of each matrix.
$$
\left[\begin{array}{lll}{0} & {0} & {8} \\ {6} & {2} & {4} \\ {1} & {3} & {6} \\ {5} & {9} & {2}\end{array}\right]
$$

Grant Westfall

Numerade Educator

Problem 12

State the dimensions of each matrix.
$$
\left[\begin{array}{rrr}{-3} & {17} & {-22} \\ {9} & {31} & {16} \\ {20} & {-15} & {4}\end{array}\right]
$$

Grant Westfall

Numerade Educator

Problem 13

State the dimensions of each matrix.
$$
\left[\begin{array}{ccccc}{17} & {-2} & {8} & {-9} & {6} \\ {5} & {11} & {20} & {-1} & {4}\end{array}\right]
$$

Grant Westfall

Numerade Educator

Problem 14

State the dimensions of each matrix.
$$
\left[\begin{array}{cc}{16} & {8} \\ {10} & {5} \\ {0} & {0}\end{array}\right]
$$

Grant Westfall

Numerade Educator

Problem 15

Solve each equation.
$$
\left[\begin{array}{ll}{4 x} & {3 y}\end{array}\right]=\left[\begin{array}{ll}{12} & {-1}\end{array}\right]
$$

Grant Westfall

Numerade Educator

Problem 16

Solve each equation.
$$
\left[\begin{array}{lll}{2 x} & {3} & {3 z}\end{array}\right]=\left[\begin{array}{lll}{5} & {3 y} & {9}\end{array}\right]
$$

Grant Westfall

Numerade Educator

Problem 17

Solve each equation.
$$
\left[\begin{array}{c}{4 x} \\ {5}\end{array}\right]=\left[\begin{array}{l}{15+x} \\ {2 y-1}\end{array}\right]
$$

Grant Westfall

Numerade Educator

Problem 18

Solve each equation.
$$
\left[\begin{array}{l}{x+3 y} \\ {3 x+y}\end{array}\right]=\left[\begin{array}{r}{-13} \\ {1}\end{array}\right]
$$

Charles Carter

Numerade Educator

Problem 19

Solve each equation.
$$
\left[\begin{array}{c}{2 x+y} \\ {x-3 y}\end{array}\right]=\left[\begin{array}{c}{5} \\ {13}\end{array}\right]
$$

Charles Carter

Numerade Educator

Problem 20

Solve each equation.
$$
\left[\begin{array}{rr}{4 x-3} & {3 y} \\ {7} & {13}\end{array}\right]=\left[\begin{array}{cc}{9} & {-15} \\ {7} & {2 z+1}\end{array}\right]
$$

Charles Carter

Numerade Educator

Problem 21

DINING OUT For Exercises 21 and $22,$ use the following information. A newspaper rated several restaurants by cost, level of service, atmosphere, and location using a scale of $\star$ being low and $\star \star \star$ being high.
(PICTURE NOT COPY)
Write a $4 \times 4$ matrix to organize this information.

Charles Carter

Numerade Educator

Problem 22

DINING OUT For Exercises 21 and $22,$ use the following information. A newspaper rated several restaurants by cost, level of service, atmosphere, and location using a scale of $\star$ being low and $\star \star \star$ being high.
(PICTURE NOT COPY)
Which restaurant would you select based on this information, and why?

Charles Carter

Numerade Educator

Problem 23

MOVIES For Exercises 23 and $24,$ use the advertisement shown at the right.
Write a matrix for the prices of movie tickets for adults, children, and seniors.

Charles Carter

Numerade Educator

Problem 24

MOVIES For Exercises 23 and $24,$ use the advertisement shown at the right.
What are the dimensions of the matrix?

Charles Carter

Numerade Educator

Problem 25

HOTELS For Exercises 25 and $26,$ use the costs for an overnight stay at a hotel that are given below. Single Room: $\$ 60$ weekday; $\$ 79$ weekend Double Room: $\$ 70$ weekday; $\$ 89$ weekend Suite: $\$ 75$ weekday; $\$ 95$ weekend
Write a $3 \times 2$ matrix that represents the cost of each room.

Charles Carter

Numerade Educator

Problem 26

HOTELS For Exercises 25 and $26,$ use the costs for an overnight stay at a hotel that are given below. Single Room: $\$ 60$ weekday; $\$ 79$ weekend Double Room: $\$ 70$ weekday; $\$ 89$ weekend Suite: $\$ 75$ weekday; $\$ 95$ weekend
Write a $2 \times 3$ matrix that represents the cost of each room.

Charles Carter

Numerade Educator

Problem 27

RESEARCH Use the Internet or other resource to find the meaning of the word matrix. How does the meaning of this word in other fields compare to its mathematical meaning?

Charles Carter

Numerade Educator

Problem 28

OPEN ENDED Give examples of a row matrix, a column matrix, a square matrix, and a zero matrix. State the dimensions of each matrix.

Charles Carter

Numerade Educator

Problem 29

CHALLENGE For Exercises 29 and $30,$ use the matrix at the right.
Study the pattern of numbers. Complete the matrix for column 6 and row 7 .

Charles Carter

Numerade Educator

Problem 30

CHALLENGE For Exercises 29 and $30,$ use the matrix at the right.
In which row and column will 100 occur?

Charles Carter

Numerade Educator

Problem 31

Writing in Math Use the information about SUVs on page 162 to explain how a matrix can help Sabrina decide which SUV to buy.

Charles Carter

Numerade Educator

Problem 32

ACT/SAT The results of a recent poll are organized in the matrix.
$$\begin{array}{l}{\text { For Against }} \\ {\text { Proposition 1 }\left[\begin{array}{cc}{1553} & {771} \\ {689} & {1633} \\ {2088} & {229}\end{array}\right]}\end{array}$$
Based on these results, which conclusion is NOT valid?
A There were 771 votes cast against Proposition 1
B More people voted against Proposition 1 than voted for Proposition 2 .
C Proposition 2 has little chance of passing.
D More people voted for Proposition 1 than for Proposition 3.

Charles Carter

Numerade Educator

Problem 33

REVIEW The chart shows an expression evaluated for four different values of $x .$
(TABLE NOT COPY)
A student concludes that for all values of $x, x^{2}+x+1$ produces a prime number. Which value of $x$ serves as a counterexample to prove this conclusion false?
$$
\begin{array}{ll}{\mathbf{F}-4} & {\mathbf{H}-2} \\ {\mathbf{G}-3} & {\mathbf{J} 4}\end{array}
$$

Charles Carter

Numerade Educator

Problem 34

Solve each system of equations.
$$
\begin{array}{l}{3 x-3 y=6} \\ {-6 y=-30} \\ {5 z-2 x=6}\end{array}
$$

Charles Carter

Numerade Educator

Problem 35

Solve each system of equations.
$$
\begin{array}{l}{3 a+2 b=27} \\ {5 a-7 b+c=5} \\ {-2 a+10 b+5 c=-29}\end{array}
$$

Charles Carter

Numerade Educator

Problem 36

Solve each system of equations.
$$
\begin{array}{l}{3 r-15 s+4 t=-57} \\ {9 r+45 s-t=26} \\ {-6 r+10 s+3 t=-19}\end{array}
$$

Charles Carter

Numerade Educator

Problem 37

BUSINESS A factory is making skirts and dresses from the same fabric. Each skirt requires 1 hour of cutting and 1 hour of sewing. Each dress requires 2 hours of cutting and 3 hours of sewing. The cutting department can cut up to 120 hours each week and the sewing department can sew up to 150 hours each week. If profits are $\$ 12$ for each skirt and $\$ 18$ for each dress, how many of each should the factory make for maximum profit?

Breanna Ollech

Numerade Educator

Problem 38

Write an equation in slope-intercept form of the line that passes through the points indicated in the table.

Charles Carter

Numerade Educator

Problem 39

Write an equation in standard form of the line that passes through the points indicated in the table.

Charles Carter

Numerade Educator

Problem 40

Find each value if $f(x)=x^{2}-3 x+2$
$$
f(3)
$$

Haley Mortell

Numerade Educator

Problem 41

Find each value if $f(x)=x^{2}-3 x+2$
$$
f(0)
$$

Charles Carter

Numerade Educator

Problem 42

Find each value if $f(x)=x^{2}-3 x+2$
$$
f(2)
$$

Charles Carter

Numerade Educator

Problem 43

Find each value if $f(x)=x^{2}-3 x+2$
$$
f(-3)
$$

Charles Carter

Numerade Educator

Problem 44

Find the value of each expression.
$$
8+(-5)
$$

Charles Carter

Numerade Educator

Problem 45

Find the value of each expression.
$$
6(-3)
$$

Charles Carter

Numerade Educator

Problem 46

Find the value of each expression.
$$
\frac{1}{2}(34)
$$

Charles Carter

Numerade Educator

Problem 47

Find the value of each expression.
$$
-5(3-18)
$$

Charles Carter

Numerade Educator