Transcript Solve a Matrix Equation

4.1, 2, 3 Perform Basic Matrix Operations
By the end you should:
1. add and subtract matrices
2. multiply by a scalar
3. solve a matrix equation
4. multiply matrices
The Matrix
Vocab:
Matrix: a rectangular arrangement of numbers in rows and columns
Dimensions: matrix with m rows and n columns
denoted
mxn
read
"m by n"
Elements: numbers inside the matrix
Equal Matrix: dimensions are the same; elements in corresponding
positions are equal; they look the same
 4 -1 5
A

0
6
3


 5 4 8 


B  4 2 7
 0 10 6 
3
C   2
1 
dimensions = ______________
name the element in the 1st row 2nd column _______
dimensions = ______________
name the element in the 3rd row 3rd column _______
dimensions = ______________
name the element in the 1st row 1st column _______
Your Turn:
1.
2.
 3 0   1 4 
 5 1   2 0  

 

 7 4   2 5 
 0 2   3 10 

 

 1 6   3 1 
a b   e
c d    g

 
f  a  e b  f 



h  c  g d  h 
 2 4  3 5
6 8   7 9 

 

a b   e
c d    g

 
f  a  e b  f 


h  c  g d  h 
 2 4  3 5
 6 8   7 9  

 

Adding and Subtracting Matrices
you can ONLY do this is they have the SAME dimensions
you will end up with ONE matrix
Your Turn:
1.
2.
 2 1 3


4  7 6 1  
 2 0 5
 4 1  2 2
3




 3 5  0 6 
Scalar Multiplication
scalar is a number
it uses the distributive property
c
a
d
e  a c


f  a d
3 2 5 3 5 2
5




 7 4  5 7 5 4 
a
a
e

f
Properties of Matrix Operations
A, B, and C are matrices with the same dimensions, and k is a scalar
• Associative Property of Addition
(A + B) + C = A + (B + C)
• Commutative Property of Addition
A+B=B+A
• Distributive Property of Addition
k(A + B) = kA + kB
• Distributive Property of Subtraction
k(A - B) = kA - kB
Solve a Matrix Equation
Solve for x and y by breaking it down
use what you know to be true
CHECK your answers!
 5 x 2  3 7    21 15 
3 





  6 4  5  y    3 24
Your Turn:
1.
  2 x 3   1 4  10 2 
2 





  5  y   3 5   16 14
2.
  3x 1  9 4  12 10 
2  





y   5 3    2 18
 4
Solve a Matrix Equation
Mary asked both the male and female players on two Basketball Teams
what color the new team uniforms should be: red, blue, or green. She
recorded the results in two matrices. Find the totals for the teams.
R
Guys 9

Girls 9
R
Guys 9

Girls 7
B G
0
9
5
 classA

4
B G
5
2
0
 classB

9
Addition of matrices and multiplication
of a matrix by a scalar
Exit Card 4.1:
1.
2.
Name: _____________________________
 4 1
3


 3 5
 4 5 x   11 2  y 12
 2 5    6 5    4 10 

 
 

Brain Teaser:
Camp Pineveiw's cook, Margaret Johnson, was just about to begin
preparing the picnic lunch for all the campers. She already knew she
needed to fill 55 bowls of the same size and capacity with the same
amount of food. When she was done, she decided to read the
guidelines for the picnic, just out of curiosity. The guidelines said:
1. Every camper gets their own bowl of soup.
2. Every two campers will get one bowl of spaghetti to share.
3. Every three campers will get one bowl of salad to share.
4. All campers are required to have their own helping of salad,
spaghetti, and soup.
After some rapid calculations, Margaret was able to figure out how
many campers were going to the picnic. Can you?
Hint
If there were only six campers, there would be six bowls of soup,
three bowls of spaghetti, and two bowls of salad