Download Matrix Operations - Dr. Taylor Math Coach

5/24/2017
Agenda
• Textbook / Web Based Resource
• Operations with Matrices
– Addition/Subtraction
– Scalar Multiplication
– Matrix Multiplication
– Identity Matrix
• Classwork
• Homework
INSERT HERE
5/24/2017
Operations
with Matrices
5/24/2017
By the end of the day:
You should know how to:
• Add/Subtract two matrices
• Multiply a matrix by a scalar
• Determine if two matrices can be
multiplied
• Determine the order of the product of two
matrices
• Multiply two matrices
• Recognize the identity matrix
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Matrix Add/Subtract
Equality of Matrices – Two Matrices are
equal if and only if they are the same size
and their corresponding entries are equal
Matrix Addition and Subtract
• Matrices must be the same size in order to
be added or subtracted
• Add/Subtract corresponding entries
• Result should be a matrix the same size
as the original
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Matrix Addition
2
-4
5
4
+
+
5
7
-2
-6
+
+
To Add Matrices,
simply add the
numbers that are in
corresponding
positions
7
0
3
1
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Matrix Subtraction
2
-4
5
4
-
-
5
7
-2
-6
-
-
To subtract matrices,
simply subtract the
numbers that are in
corresponding
positions
-3
-8
7
13
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Matrix Addition and
Subtraction
You Try These on Your Own:
1. INSERT YOUR PROBLEMS HERE
5/24/2017
Scalar Multiplication
Scalar Multiplication
• Multiplying an entire matrix by a factor
• Multiply each entry by the Scalar factor
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Scalar Multiplication
3 
2
-4


5
7


To multiply by a
scalar, multiply
each entry.
6
-12
15
21
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Classwork
2) x = 5, y = -8
6)a) 4 5
L
O
M
P
4
1
N Q
b) L10 3O
M
P

12
9
N Q
c) L21 12O
M
P

12
15
N Q
d) L27 10O
M
P

28
23
N Q
4) x = -4, y = 9
8)a) 12 8 1 1 4
L
O
M
P
0
7

1
6
0
N
Q
b) L0 8 7 3 2O
M
P

8

3
3
4

4
N
Q
c) L18 24 9 6 3 O
M
P

12
6
3
15

6
N
Q
d) L6 24 17 8 3 O
M
P

20

4
7
13

10
N
Q
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Matrix Multiplication
Matrix Multiplication
• Number of columns in first matrix must be
the same as the number of rows in the
second matrix
• Answer will have same number of rows as
the first matrix and the same number of
columns as the second matrix
• Find each entry in the answer matrix by
working across a row in the first matrix and
down a column in the second matrix. Add
the products together to get the entry
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Matrix Multiplication
3
 -1

-2 5
4 -3
2x3
1
 
-4

 
 2



4
=
5

3




+


+
1, 1


+

+

+

1, 2
+

2, 1
3x2
To Multiply
Matrices: Multiply
Row by Column!!!

+

+

2, 2



2x2
=



21
26
1, 1
1, 2
-23
-2
2, 1
2, 2



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Matrix Multiplication
You Try These on Your Own:
1. INSERT YOUR PROBLEMS HERE
5/24/2017
Identity Matrix
The Identity Matrix:
• Is a Square Matrix
• Has entries of 1 across diagonal
• Has entries of 0 everywhere else
L
M
10
M
M
26
N
22) 3
O
P
16 P
46 P
Q
4
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Identity Matrix
You Try These on Your Own:
1. INSERT YOUR PROBLEMS HERE
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It’s the end of the day:
Do you know how to:
• Add/Subtract two matrices?
• Multiply a matrix by a scalar?
• Determine if two matrices can be
multiplied?
• Determine the order of the product of two
matrices?
• Multiply two matrices?
• Recognize the identity matrix?






5/24/2017
Homework
Study:
INSERT HERE
Do:
INSERT HERE
Read & Take Notes:
INSERT HERE
5/24/2017
Resource Credits
Justin Bohannon