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Section 2.5 – Multiplication of Matrices
1
Section 2.5
Multiplication of Matrices
If A is a matrix of size
m
x
n
and B is a matrix of size
n
x
p
then the product AB is defined
and is a matrix of size
m
x
p
.
So, two matrices can be multiplied if and only if the number of columns in the first
matrix is equal to the number of rows in the second matrix.
How to Multiply Two Matrices
The element in the
i
th row and
j
th column of AB is found by multiplying each element in
the
i
th row of A by the corresponding element in the
j
th column of B and adding the
products.
Example 1:
Your stock holdings are given by the row matrix (or vector)
GM
IBM
BAC
()
200
400
700
=
A
At the close of trading on a certain day, the prices (in dollars per share) of these stocks
(GM, IBM, BAC, respectively) are
⎟
⎟
⎟
⎠
⎞
⎜
⎜
⎜
⎝
⎛
=
42
120
50
B
What is the total value of your holdings as of that day?
Example 2:
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 Fall '08
 CONSTANTE
 Math, Multiplication, Matrices

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