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ATRIX
M
ULTIPLICATION
AND
THE
I
DENTITY
M
ATRIX
Matrix multiplication has many purposes.
To multiply two matrices, multiply the elements of
each row of one matrix by the elements of each column of the other matrix.
(Think over and
down).
+
+
+
+
+
+
+
+
=
×
fl
ek
dj
fi
eh
dg
cl
ak
aj
ci
bh
ag
l
i
k
h
j
g
f
e
d
c
b
a
Therefore to be able to multiply two matrices, the number of rows of the first matrix must
equal the number of columns of the second matrix.
Ex
.
[
]
2
1 3 4
4
5

×
=
The result of multiplying a
3
1
×
matrix by a
1
3
×
is a
1
1
×
matrix.
Therefore, the result of multiplying an
p
m
×
matrix by a
n
p
×
matrix is an
n
m
×
matrix.
Ex
.

×
8
1
2
7
6
2
0
1
=
Note that the result of multiplying matrix A by matrix B is not the same as multiplying matrix
B by matrix A.
Ex
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