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Are the rows of a
matrix horizontal
or vertical?
Horizontal
Horizontal entries
of a matrix are
called rows. What
are the vertical
entries called?
Columns
How many rows
does the following
matrix have?
 3 9 0
 4 5 8


  9 4 5 
Three
What are the
dimensions of the
following matrix?
2
 9 5 3
1x4
What will be the
dimensions of the
product of the following
two matrices?
4


2 7 4 5
8 
1x1
Add the following
matrices.
3  6 3 7

 4 0  4 8 

 

6 1
8 8


Subtract the
following matrices.
3  6  3  7

4 0   0

9

 
6 1 
 4  9


Solve:
5  2 2   4 1 5 
6  5 0   7 2 7 

 

8 6 1  8 0 2
 9  1 7
13  3 7 


16 6 3
Solve:
5  2 2   4 1 5 
6  5 0   7 2 7 

 

8 6 1  8 0 2
 1  3  3
 1  7  7 


 0
6  1 
Solve:
5  2 2   4 1 5 




2 6  5 0   7 2 7 
8 6 1  8 0 2
6  5  1 
5  12  7 


8 12
0 
If you multiply a
3x2 matrix with a
2x1 matrix, what
will the dimensions
of the product be?
3x1
Is it possible to
multiply a 3x2 matrix
with a 2x1 matrix?
How do you know?
Yes, because the
“2’s” are equal.
Multiply:
2 1 3 0

0 5 4 1

 

10 1
20 5


Multiply:
2 0 
1  1  0

  3


3 4 
0
  3
 
 12 
Solve:
2 3 0 3 0
2




4
1
1
4
2

 

6 36 12
2 32 4 


Solve:
x  3 y  16
x  2 y  31
x=25
y=-3
Solve:
 9  3 1  x   7 
 1 1 1   y     3

    
16 4 1  z   21
x=1
y=3
z=-7
Solve:
p  2q  7
3 p  4q  11
p=-3
q=5
Solve:
4 x  y  z  5
2 x  2 y  3z  10
5x  2 y  6 z  1
x=-1
y=3
z=2
Solve:
7 w  3x  2 z  41
 2w  x  z  13
4w  y  2 z  12
w  3z  1
 5 
2



15


2


3


 1 
 2 
What is the
additive identity of
a 2x2 matrix?
0 0 
0 0 


What is the
multiplicative
identity of a 2x2
matrix.
1 0 
0 1 


Find the inverse of
the following
matrix (in fraction
form): 3  1
4


0
0 1 
4


3
 1

4
True of False:
1
A A I
and
AA
1
I
True
Find the inverse of
the following
matrix (in fraction
2 3 1

form) 

3
2
3


0 1 4
7 
11
 5
23
23
 23
8
3 
 12
23
23
23
 3

5
2
 23

23
23 
Is matrix
multiplication
commutative?
No
Is matrix addition
commutative?
Yes
How many rows
does a 3x5 matrix
have?
Three
How many
columns does a
8x12 matrix have?
12
Create AX=B matrices
for the following
systems of equations.
3x  y  2 z  1
2 x  y  z  3
x  y  4 z  3
2   x  1 
3 1
2  1 1    y    3

    
1 1  4  z   3
Make your wager
Final Answer
Final Question