unit 2 day 1 matrices - ghhsicm.weebly.com · b) column matrix: only has 1 column. c) square...
TRANSCRIPT
![Page 1: Unit 2 Day 1 MATRICES - ghhsicm.weebly.com · b) Column matrix: only has 1 column. c) Square matrix: has the same number of rows and columns. d) Zero matrix: contains all zeros. Ex)](https://reader031.vdocuments.us/reader031/viewer/2022020105/5e15431d47954832443dfd35/html5/thumbnails/1.jpg)
Unit 2 Day 1
MATRICES
MATRIX OPERATIONS
![Page 2: Unit 2 Day 1 MATRICES - ghhsicm.weebly.com · b) Column matrix: only has 1 column. c) Square matrix: has the same number of rows and columns. d) Zero matrix: contains all zeros. Ex)](https://reader031.vdocuments.us/reader031/viewer/2022020105/5e15431d47954832443dfd35/html5/thumbnails/2.jpg)
Warm-UpBasic Matrix Practice
2
1 2
2. 5 4 1
0 5
x
y
x
4 6 51.
6 3 7 3
a
a
1 3 2 2 1 53.
4 0 5 6 4 3
b
c
3 04. 3
4 5
t
q
![Page 3: Unit 2 Day 1 MATRICES - ghhsicm.weebly.com · b) Column matrix: only has 1 column. c) Square matrix: has the same number of rows and columns. d) Zero matrix: contains all zeros. Ex)](https://reader031.vdocuments.us/reader031/viewer/2022020105/5e15431d47954832443dfd35/html5/thumbnails/3.jpg)
4 6 51.
6 3 7 3
a
a
1 3 2 2 1 53.
4 0 5 6 4 3
b
c
2 5
7 6 0
a
a
1 4 2 5
4 6 4 8
b
c
Warm-Up ANSWERS! Matrix Addition & Subtraction:
![Page 4: Unit 2 Day 1 MATRICES - ghhsicm.weebly.com · b) Column matrix: only has 1 column. c) Square matrix: has the same number of rows and columns. d) Zero matrix: contains all zeros. Ex)](https://reader031.vdocuments.us/reader031/viewer/2022020105/5e15431d47954832443dfd35/html5/thumbnails/4.jpg)
3 04. 3
4 5
t
q
2
1 2
2. 5 4 1
0 5
x
y
x
Warm-Up ANSWERS! Scalar Multiplication:
9 0
12 15
t
q
2
5 10 5
20 5 5
0 25 5
x
y
x
![Page 5: Unit 2 Day 1 MATRICES - ghhsicm.weebly.com · b) Column matrix: only has 1 column. c) Square matrix: has the same number of rows and columns. d) Zero matrix: contains all zeros. Ex)](https://reader031.vdocuments.us/reader031/viewer/2022020105/5e15431d47954832443dfd35/html5/thumbnails/5.jpg)
Questions About HW?
Questions About Matrices
Basics HW?
![Page 6: Unit 2 Day 1 MATRICES - ghhsicm.weebly.com · b) Column matrix: only has 1 column. c) Square matrix: has the same number of rows and columns. d) Zero matrix: contains all zeros. Ex)](https://reader031.vdocuments.us/reader031/viewer/2022020105/5e15431d47954832443dfd35/html5/thumbnails/6.jpg)
Tonights HW
Is Packet p. 1-2
A heads-up…
The HW is not in order in the
packet, so be sure to refer
to your outline this unit.
![Page 7: Unit 2 Day 1 MATRICES - ghhsicm.weebly.com · b) Column matrix: only has 1 column. c) Square matrix: has the same number of rows and columns. d) Zero matrix: contains all zeros. Ex)](https://reader031.vdocuments.us/reader031/viewer/2022020105/5e15431d47954832443dfd35/html5/thumbnails/7.jpg)
Unit 2 Day 1
NOTES Part 1
BASIC MATRIX OPERATIONS
& APPLICATIONS
![Page 8: Unit 2 Day 1 MATRICES - ghhsicm.weebly.com · b) Column matrix: only has 1 column. c) Square matrix: has the same number of rows and columns. d) Zero matrix: contains all zeros. Ex)](https://reader031.vdocuments.us/reader031/viewer/2022020105/5e15431d47954832443dfd35/html5/thumbnails/8.jpg)
Remember…Matrix: a rectangular array of numbers or variables used to organize data.
2 4
3 5
1 6
A
Typically, we name matrices with capital letters!
The numbers in the matrix are called elements. There are 6 elements in this matrix.
![Page 9: Unit 2 Day 1 MATRICES - ghhsicm.weebly.com · b) Column matrix: only has 1 column. c) Square matrix: has the same number of rows and columns. d) Zero matrix: contains all zeros. Ex)](https://reader031.vdocuments.us/reader031/viewer/2022020105/5e15431d47954832443dfd35/html5/thumbnails/9.jpg)
Remember…Matrix dimensions tell how many ROWS & COLUMNS there are in the matrix.
Dimensions & Notation
A 3 x 2
REMEMBER:RC colaRows by columns
Rows run horizontally & columns run vertically.
The dimensions of two matrices can determine whether or not they may be added, subtracted, or multiplied.
2 4
3 5
1 6
A
![Page 10: Unit 2 Day 1 MATRICES - ghhsicm.weebly.com · b) Column matrix: only has 1 column. c) Square matrix: has the same number of rows and columns. d) Zero matrix: contains all zeros. Ex)](https://reader031.vdocuments.us/reader031/viewer/2022020105/5e15431d47954832443dfd35/html5/thumbnails/10.jpg)
A matrix of m rows and n columns is called a matrix with dimensions m x n.
2 3 4
1.) 11
2
3 8 9
2.) 2 5
6 7 8
103.)
7
4.) 3 4
2 X 3 3 X 3
2 X 11 X 2
You Try Examples: Find the dimensions.
![Page 11: Unit 2 Day 1 MATRICES - ghhsicm.weebly.com · b) Column matrix: only has 1 column. c) Square matrix: has the same number of rows and columns. d) Zero matrix: contains all zeros. Ex)](https://reader031.vdocuments.us/reader031/viewer/2022020105/5e15431d47954832443dfd35/html5/thumbnails/11.jpg)
Matrix Position
We can give the location of an element in a matrix by naming its row, then its column.
2 4 8 4
3 5 6 3
1 6 2 0
3 is in position ____
6 is in position ____
4 is in position ____
-2 is in position _____
k24
k32
k14
k33
![Page 12: Unit 2 Day 1 MATRICES - ghhsicm.weebly.com · b) Column matrix: only has 1 column. c) Square matrix: has the same number of rows and columns. d) Zero matrix: contains all zeros. Ex)](https://reader031.vdocuments.us/reader031/viewer/2022020105/5e15431d47954832443dfd35/html5/thumbnails/12.jpg)
Why use matrices?
Matrix algebra makes mathematical expression and computation easier.
It allows you to get rid of cumbersome notation, concentrate on the concepts involved and understand where your results come from.
Matrices are used to represent real-world datasuch as the habits or traits of populations.
![Page 13: Unit 2 Day 1 MATRICES - ghhsicm.weebly.com · b) Column matrix: only has 1 column. c) Square matrix: has the same number of rows and columns. d) Zero matrix: contains all zeros. Ex)](https://reader031.vdocuments.us/reader031/viewer/2022020105/5e15431d47954832443dfd35/html5/thumbnails/13.jpg)
Special MatricesSome matrices have special names
because of what they look like.
a) Row matrix: only has 1 row.
b) Column matrix: only has 1 column.
c) Square matrix: has the same number of rows
and columns.
d) Zero matrix: contains all zeros.
) 3 4Ex
10)
7Ex
10 2)
7 3Ex
) 0 0Ex
![Page 14: Unit 2 Day 1 MATRICES - ghhsicm.weebly.com · b) Column matrix: only has 1 column. c) Square matrix: has the same number of rows and columns. d) Zero matrix: contains all zeros. Ex)](https://reader031.vdocuments.us/reader031/viewer/2022020105/5e15431d47954832443dfd35/html5/thumbnails/14.jpg)
Remember…Matrix Addition & Subtraction
You can add or subtract matrices if they have the same
dimensions (same number of rows and columns).
To do this, you add (or subtract) the corresponding
numbers (numbers in the same positions).
If a matrix operation is not possible for a problem, the
solution is called undefined.
Ex:
2 41 2 3
5 00 1 3
1 3
Undefined
![Page 15: Unit 2 Day 1 MATRICES - ghhsicm.weebly.com · b) Column matrix: only has 1 column. c) Square matrix: has the same number of rows and columns. d) Zero matrix: contains all zeros. Ex)](https://reader031.vdocuments.us/reader031/viewer/2022020105/5e15431d47954832443dfd35/html5/thumbnails/15.jpg)
Properties of Matrix Addition
Matrix addition IS commutative
A + B = B + A
Matrix addition IS associative
A + (B + C) = (A + B) + C
![Page 16: Unit 2 Day 1 MATRICES - ghhsicm.weebly.com · b) Column matrix: only has 1 column. c) Square matrix: has the same number of rows and columns. d) Zero matrix: contains all zeros. Ex)](https://reader031.vdocuments.us/reader031/viewer/2022020105/5e15431d47954832443dfd35/html5/thumbnails/16.jpg)
Remember…Scalar Multiplication
2 4
4 5 0
1 3
To do this, multiply each entry in the matrix by the number outside (called the scalar).
This is like distributing a number to a polynomial.
Example:
8 16
20 0
4 12
![Page 17: Unit 2 Day 1 MATRICES - ghhsicm.weebly.com · b) Column matrix: only has 1 column. c) Square matrix: has the same number of rows and columns. d) Zero matrix: contains all zeros. Ex)](https://reader031.vdocuments.us/reader031/viewer/2022020105/5e15431d47954832443dfd35/html5/thumbnails/17.jpg)
Unit 2 Day 1
NOTES Part 2
MATRIX MULTIPLICATION
![Page 18: Unit 2 Day 1 MATRICES - ghhsicm.weebly.com · b) Column matrix: only has 1 column. c) Square matrix: has the same number of rows and columns. d) Zero matrix: contains all zeros. Ex)](https://reader031.vdocuments.us/reader031/viewer/2022020105/5e15431d47954832443dfd35/html5/thumbnails/18.jpg)
Matrix Multiplication
Matrix Multiplication is NOT Commutative!
Order matters!
You can multiply matrices only if the number of
columns in the first matrix equals the number
of rows in the second matrix.
2 3
5 6
9 7
2 columns
2 rows1 2 0
3 4 5
3 x 2 2 x 3 = 3 x 3resulting matrix
![Page 19: Unit 2 Day 1 MATRICES - ghhsicm.weebly.com · b) Column matrix: only has 1 column. c) Square matrix: has the same number of rows and columns. d) Zero matrix: contains all zeros. Ex)](https://reader031.vdocuments.us/reader031/viewer/2022020105/5e15431d47954832443dfd35/html5/thumbnails/19.jpg)
Matrix Multiplication
Take the numbers in the first row of matrix #1. Multiply
each number by its corresponding number in the first
column of matrix #2. Total these products.
2 3
5 6
9 7
1 2 0
3 4 5
2 1 3 311
Do 1st ● 1st + 2nd ● 2nd +…
The result, 11, goes in row 1, column 1 of the answer. Repeat with row 1, column 2; row 1 column 3; row 2, column 1; ...
Continued on the next slide….
![Page 20: Unit 2 Day 1 MATRICES - ghhsicm.weebly.com · b) Column matrix: only has 1 column. c) Square matrix: has the same number of rows and columns. d) Zero matrix: contains all zeros. Ex)](https://reader031.vdocuments.us/reader031/viewer/2022020105/5e15431d47954832443dfd35/html5/thumbnails/20.jpg)
Let’s Try!
2 3
5 6
9 7
1 2 0
3 4 5
![Page 21: Unit 2 Day 1 MATRICES - ghhsicm.weebly.com · b) Column matrix: only has 1 column. c) Square matrix: has the same number of rows and columns. d) Zero matrix: contains all zeros. Ex)](https://reader031.vdocuments.us/reader031/viewer/2022020105/5e15431d47954832443dfd35/html5/thumbnails/21.jpg)
Let’s Try Answer!
2 3
5 6
9 7
1 2 0
3 4 5
11 8 15
13 34 30
12 46 35
![Page 22: Unit 2 Day 1 MATRICES - ghhsicm.weebly.com · b) Column matrix: only has 1 column. c) Square matrix: has the same number of rows and columns. d) Zero matrix: contains all zeros. Ex)](https://reader031.vdocuments.us/reader031/viewer/2022020105/5e15431d47954832443dfd35/html5/thumbnails/22.jpg)
You Try!2 1 3 9 2
3 4 5 7 6
![Page 23: Unit 2 Day 1 MATRICES - ghhsicm.weebly.com · b) Column matrix: only has 1 column. c) Square matrix: has the same number of rows and columns. d) Zero matrix: contains all zeros. Ex)](https://reader031.vdocuments.us/reader031/viewer/2022020105/5e15431d47954832443dfd35/html5/thumbnails/23.jpg)
You Try!Answer
2 1 3 9 2
3 4 5 7 6
2(3) + -1(5) 2(-9) + -1(7) 2(2) + -1(-6)
3(3) + 4(5) 3(-9) + 4(7) 3(2) + 4(-6)
1 25 10
29 1 18
2 x 2 2 x 3
![Page 24: Unit 2 Day 1 MATRICES - ghhsicm.weebly.com · b) Column matrix: only has 1 column. c) Square matrix: has the same number of rows and columns. d) Zero matrix: contains all zeros. Ex)](https://reader031.vdocuments.us/reader031/viewer/2022020105/5e15431d47954832443dfd35/html5/thumbnails/24.jpg)
Matrix Multiplication
5
2A
8
45
60
2 1
9 0
10 5
B
2 15
9 02
10 5
BA
Find AB and BA given and
AB is undefined. A 2 x 1 and 3 x 2 cannot be multiplied.
![Page 25: Unit 2 Day 1 MATRICES - ghhsicm.weebly.com · b) Column matrix: only has 1 column. c) Square matrix: has the same number of rows and columns. d) Zero matrix: contains all zeros. Ex)](https://reader031.vdocuments.us/reader031/viewer/2022020105/5e15431d47954832443dfd35/html5/thumbnails/25.jpg)
Matrix Multiplication Properties
Matrix multiplication is NOT commutative
AB≠BA
Matrix multiplication IS associative
A(BC)=(AB)C
Matrix multiplication IS distributive
A(B+C)=AB+AC(A+B)C=AC+BC
![Page 26: Unit 2 Day 1 MATRICES - ghhsicm.weebly.com · b) Column matrix: only has 1 column. c) Square matrix: has the same number of rows and columns. d) Zero matrix: contains all zeros. Ex)](https://reader031.vdocuments.us/reader031/viewer/2022020105/5e15431d47954832443dfd35/html5/thumbnails/26.jpg)
Packet p. 2 #1Matrix Applications
Two softball teams submit equipment lists for the season.Women’s Team: 12 bats, 45 balls, 15 uniforms
Men’s Team: 15 bats, 38 balls 17 uniforms
Each bat costs $21, each ball costs $4, and each uniform costs $30.
Use matrix multiplication to find the total cost of equipment for each team.
![Page 27: Unit 2 Day 1 MATRICES - ghhsicm.weebly.com · b) Column matrix: only has 1 column. c) Square matrix: has the same number of rows and columns. d) Zero matrix: contains all zeros. Ex)](https://reader031.vdocuments.us/reader031/viewer/2022020105/5e15431d47954832443dfd35/html5/thumbnails/27.jpg)
ApplicationAnswer
![Page 28: Unit 2 Day 1 MATRICES - ghhsicm.weebly.com · b) Column matrix: only has 1 column. c) Square matrix: has the same number of rows and columns. d) Zero matrix: contains all zeros. Ex)](https://reader031.vdocuments.us/reader031/viewer/2022020105/5e15431d47954832443dfd35/html5/thumbnails/28.jpg)
Practice on Packet p. 2
Matrix Applications Handout #2 and 3
![Page 29: Unit 2 Day 1 MATRICES - ghhsicm.weebly.com · b) Column matrix: only has 1 column. c) Square matrix: has the same number of rows and columns. d) Zero matrix: contains all zeros. Ex)](https://reader031.vdocuments.us/reader031/viewer/2022020105/5e15431d47954832443dfd35/html5/thumbnails/29.jpg)
Unit 2 Day 1
NOTES
MATRIX APPLICATIONS
![Page 30: Unit 2 Day 1 MATRICES - ghhsicm.weebly.com · b) Column matrix: only has 1 column. c) Square matrix: has the same number of rows and columns. d) Zero matrix: contains all zeros. Ex)](https://reader031.vdocuments.us/reader031/viewer/2022020105/5e15431d47954832443dfd35/html5/thumbnails/30.jpg)
Application Example 1(on power point slide handout)
Ex 1) Last year at Green Hope, there were 214 senior girls, 243 senior guys, 245 junior girls, 233 junior guys, 258 sophomore girls, 288 sophomore guys, and 345 freshman girls, and 303 freshman guys. At Cary, there were 223 senior girls, 252 senior guys, 250 junior girls, 200 junior guys, 260 sophomore girls, 248 sophomore guys, and 352 freshman girls, and 333 freshman guys.
a) Write matrices G and C that represent the population of each school.
b) Add these two together. What does this new matrix represent?
![Page 31: Unit 2 Day 1 MATRICES - ghhsicm.weebly.com · b) Column matrix: only has 1 column. c) Square matrix: has the same number of rows and columns. d) Zero matrix: contains all zeros. Ex)](https://reader031.vdocuments.us/reader031/viewer/2022020105/5e15431d47954832443dfd35/html5/thumbnails/31.jpg)
Application Example 2(on power point slide handout)
Last year at Green Hope, there were 214 senior girls, 243 senior guys, 245 junior girls, 233 junior guys, 258 sophomore girls, 288 sophomore guys, and 345 freshman girls, and 303 freshman guys.
Ex 2) Use the matrix of Green Hope students from the last example. If a college claims it is 5 times as large as our school, with students being distributed the same by year and gender, create a new matrix that shows the number of students at the college.
![Page 32: Unit 2 Day 1 MATRICES - ghhsicm.weebly.com · b) Column matrix: only has 1 column. c) Square matrix: has the same number of rows and columns. d) Zero matrix: contains all zeros. Ex)](https://reader031.vdocuments.us/reader031/viewer/2022020105/5e15431d47954832443dfd35/html5/thumbnails/32.jpg)
YOU TRY Application: (on power point slide handout)
The A-Plus auto parts store has two outlets, one in Greensboro and one in Charlotte. Among other things, it sells wiper blades, windshield cleaning fluid, and floor mats. The monthly sales of those products are given below.
January Ss G’boro Charlotte
Wiper Blades 20 15
Cleaning Fluid 10 12
Floor Mats 8 4
February Ss G’boro Charlotte
Wiper Blades 23 12
Cleaning Fluid 8 12
Floor Mats 4 5
1) Use matrix arithmetic to calculate the change in sales of each product in each store from January to February. Show your matrix operations. Label your matrices.
![Page 33: Unit 2 Day 1 MATRICES - ghhsicm.weebly.com · b) Column matrix: only has 1 column. c) Square matrix: has the same number of rows and columns. d) Zero matrix: contains all zeros. Ex)](https://reader031.vdocuments.us/reader031/viewer/2022020105/5e15431d47954832443dfd35/html5/thumbnails/33.jpg)
YOU TRY Application: (on power point slide handout)The January revenue generated by sales in the Greensboro and Charlotte branches for the A-Plus auto parts store was as follows:
2) Suppose the January revenue at the Greensboro A-Plus store was $140 for wiper blades, $30 for cleaning fluid, and $96 for floor mats. The January revenue for the Charlotte store was $105 for wiper blades, $36 for cleaning fluid, and $48 for floor mats.
a) Write a matrix to represent the data above. Label it.b) If the US dollar was worth $0.76 Canadian dollars at the time, compute the revenue in Canadian dollars using matrix arithmetic. Show your matrix operations. Label your matrices.
![Page 34: Unit 2 Day 1 MATRICES - ghhsicm.weebly.com · b) Column matrix: only has 1 column. c) Square matrix: has the same number of rows and columns. d) Zero matrix: contains all zeros. Ex)](https://reader031.vdocuments.us/reader031/viewer/2022020105/5e15431d47954832443dfd35/html5/thumbnails/34.jpg)
Application ANSWERS: The A-Plus auto parts store has two outlets, one in Greensboro and one in Charlotte. Among other things, it sells
wiper blades, windshield cleaning fluid, and floor mats. The monthly sales of those products are given below.
January Ss G’boro Charlotte
Wiper Blades 20 15
Cleaning Fluid 10 12
Floor Mats 8 4
February Ss G’boro Charlotte
Wiper Blades 23 12
Cleaning Fluid 8 12
Floor Mats 4 5
Use matrix arithmetic to calculate the change in sales of each product in each store from January to February. Label your matrices.
23 12 20 15
8 12 10 12
4 5 8 4
Gb Ch Gb Ch
WB
F J CF
FM
3 3
2 0
4 1
Gb Ch
WB
F J CF
FM
![Page 35: Unit 2 Day 1 MATRICES - ghhsicm.weebly.com · b) Column matrix: only has 1 column. c) Square matrix: has the same number of rows and columns. d) Zero matrix: contains all zeros. Ex)](https://reader031.vdocuments.us/reader031/viewer/2022020105/5e15431d47954832443dfd35/html5/thumbnails/35.jpg)
Application of Scalar Multiplication ANSWERS: Suppose the January revenue at the Greensboro A-Plus store was $140 for wiper blades, $30 for cleaning fluid, and $96 for floor mats. The January revenue for the Charlotte store was $105 for wiper blades, $36 for cleaning fluid, and $48 for floor mats.
a) Write a matrix to represent the data above. Label it.
b) If the US dollar was worth $0.76 Canadian dollars at the time, compute the revenue in Canadian dollars using matrix arithmetic. Show your matrix operations. Label your matrices.
140 105
. 0.76 0.76 30 36
96 48
Gb Ch
Can Value J
106.4 79.8
22.8 27.36
72.96 36.48
Gb Ch
WB
CF
CM
140 105
30 36
96 48
Gb Ch
WB
J CF
CM
![Page 36: Unit 2 Day 1 MATRICES - ghhsicm.weebly.com · b) Column matrix: only has 1 column. c) Square matrix: has the same number of rows and columns. d) Zero matrix: contains all zeros. Ex)](https://reader031.vdocuments.us/reader031/viewer/2022020105/5e15431d47954832443dfd35/html5/thumbnails/36.jpg)
Homework
Packet p. 1 and 2
![Page 37: Unit 2 Day 1 MATRICES - ghhsicm.weebly.com · b) Column matrix: only has 1 column. c) Square matrix: has the same number of rows and columns. d) Zero matrix: contains all zeros. Ex)](https://reader031.vdocuments.us/reader031/viewer/2022020105/5e15431d47954832443dfd35/html5/thumbnails/37.jpg)
Extra practice on next slides…
![Page 38: Unit 2 Day 1 MATRICES - ghhsicm.weebly.com · b) Column matrix: only has 1 column. c) Square matrix: has the same number of rows and columns. d) Zero matrix: contains all zeros. Ex)](https://reader031.vdocuments.us/reader031/viewer/2022020105/5e15431d47954832443dfd35/html5/thumbnails/38.jpg)
Identify each matrix element.
K =
Organizing Data Into Matrices
3 –1 –8 5
1 8 4 9
8 –4 7 –5
a. k12 b. k32 c. k23 d. k34
Element k12 is –1. Element k32 is –4.
a. K =
k12 is the element in the first
row and second column.
3 –1 –8 5
1 8 4 9
8 –4 7 –5
b. K =
k32 is the element in the third
row and second column.
3 –1 –8 5
1 8 4 9
8 –4 7 –5
![Page 39: Unit 2 Day 1 MATRICES - ghhsicm.weebly.com · b) Column matrix: only has 1 column. c) Square matrix: has the same number of rows and columns. d) Zero matrix: contains all zeros. Ex)](https://reader031.vdocuments.us/reader031/viewer/2022020105/5e15431d47954832443dfd35/html5/thumbnails/39.jpg)
Matrix Addition
Examples
2 4 1 0
5 0 2 1
1 3 3 3
Ex 1:
2 41 2 3
5 00 1 3
1 3
Ex 2:
![Page 40: Unit 2 Day 1 MATRICES - ghhsicm.weebly.com · b) Column matrix: only has 1 column. c) Square matrix: has the same number of rows and columns. d) Zero matrix: contains all zeros. Ex)](https://reader031.vdocuments.us/reader031/viewer/2022020105/5e15431d47954832443dfd35/html5/thumbnails/40.jpg)
Matrix Addition
Example ANSWERS
2 4 1 0
5 0 2 1
1 3 3 3
Ex 1:
3 4
7 1
2 0
2 41 2 3
5 00 1 3
1 3
Ex 2:
Undefined
![Page 41: Unit 2 Day 1 MATRICES - ghhsicm.weebly.com · b) Column matrix: only has 1 column. c) Square matrix: has the same number of rows and columns. d) Zero matrix: contains all zeros. Ex)](https://reader031.vdocuments.us/reader031/viewer/2022020105/5e15431d47954832443dfd35/html5/thumbnails/41.jpg)
The table shows information on ticket sales for
a new movie that is showing at two theaters. Sales are
for children (C) and adults (A).
Adding and Subtracting Matrices
a. Write two 2 2 matrices to represent matinee and evening sales.
Theater C A C A
1 198 350 54 439
2 201 375 58 386
b. Find the combined sales for the two showings.
![Page 42: Unit 2 Day 1 MATRICES - ghhsicm.weebly.com · b) Column matrix: only has 1 column. c) Square matrix: has the same number of rows and columns. d) Zero matrix: contains all zeros. Ex)](https://reader031.vdocuments.us/reader031/viewer/2022020105/5e15431d47954832443dfd35/html5/thumbnails/42.jpg)
The table shows information on ticket sales for a new
movie that is showing at two theaters. Sales are for children (C)
and adults (A).
ANSWERS Adding and Subtracting Matrices
a. Write two 2 2 matrices to represent matinee and evening sales.
Theater 1 198 350
Theater 2 201 375
MatineeC A
4-2
Theater 1 54 439
Theater 2 58 386
EveningC A
Theater C A C A
1 198 350 54 439
2 201 375 58 386
![Page 43: Unit 2 Day 1 MATRICES - ghhsicm.weebly.com · b) Column matrix: only has 1 column. c) Square matrix: has the same number of rows and columns. d) Zero matrix: contains all zeros. Ex)](https://reader031.vdocuments.us/reader031/viewer/2022020105/5e15431d47954832443dfd35/html5/thumbnails/43.jpg)
(continued)
b. Find the combined sales for the two showings.
198 350
201 375+
54 439
58 386=
198 + 54 350 + 439
201 + 58 375 + 386
=Theater 1 252 789
Theater 2 259 761
C A
4-2
ANSWERS Adding and Subtracting Matrices
![Page 44: Unit 2 Day 1 MATRICES - ghhsicm.weebly.com · b) Column matrix: only has 1 column. c) Square matrix: has the same number of rows and columns. d) Zero matrix: contains all zeros. Ex)](https://reader031.vdocuments.us/reader031/viewer/2022020105/5e15431d47954832443dfd35/html5/thumbnails/44.jpg)
Adding & Subtracting MatricesYou can perform matrix addition on matrices with equal dimensions.
a. b.9 0
–4 6 +0 0
0 0
3 –8
–5 1 +–3 8
5 –1
= 9 + 0 0 + 0
–4 + 0 6 + 0=
3 + (–3) –8 + 8
–5 + 5 1 + (–1)
= 9 0
–4 6=
0 0
0 0
4-2