c Kendra Kilmer August 18, 2011
Section 2.5  Multiplication of Matrices
How to Multiply Matrices (
C
=
AB
):
(a) Check to see if the number of columns of matrix
A
is equal to the number of rows in matrix
B
. If this condition
is satisfied, the multiplication is a valid operation. The resulting matrix
C
will have the same number of rows
as
A
and the same number of columns as
B
.
(b) Compute each entry in the resulting matrix
C
. The entry
c
i j
is found by using the
i
th row of matrix
A
and the
j
th column of matrix
B
as shown in the next example.
Example 1:
Let
A
=
1
2
3
4
B
=
4
2
1
3
Find
C
where
C
=
AB
.
Note: In general,
AB
6
=
BA
Example 2:
Given the following matrices with given dimensions, determine whether each of the following is a
valid matrix operation.
A
2
×
3
B
3
×
5
C
5
×
2
D
2
×
3
a)
AB

C
b) 3
AC

D
c)
CD

5
B
T
d)
DA

3
C
e)
D

BC
12
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c Kendra Kilmer August 18, 2011
Definition:
The
identity matrix
of size
n
has
n
rows and
n
columns. It has 1’s along the main diagonal
and 0’s everywhere else.
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 Fall '08
 JillZarestky
 Multiplication, Matrices, Santa Cruz, College Station, Kendra Kilmer

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