General Contents
Detailed Contents
Index
Matrix Multiplication:
1 x 3 by 3 x 2
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Find the product
AB = C
, where
A
=
and
B
=
We'll be talking about rows and columns, so let's be sure which is which. Is a column left-right or up-and-down?
Up-down.
These matrices have different numbers of rows and columns. Can they really be multiplied?
Yes they can.
What is the requirement on the number of rows and columns of
A
and
B
?
The only requirement is that the number of columns in the first matrix must be the same as the number of rows in the second.
Will the result of
AB = C
be a number or a matrix?
A matrix.
How many rows will
C
have?
It will have the same number of rows as the first matrix has.
How many is that here?
One.
How many columns will C have?
It will have the same number of columns as the second matrix has.
How many is that here?
Two.
Use C
11
and C
12
to represent the elements of
C
. Show how
C
will look.
Now we can set up our problem:
The bold type indicates how we obtain C
11
. Show the details with the numerical values.
We get C
11
= 4*1 + 1*3 + 5*(–2) = –3
Which column of
B
is involved in C
12
?
The second.
Indicate this with bolding on the matrices.
Show the details with the numerical values.
We get C
12
= 4*(–4) + 1*2 + 5*(–3) = –29
Combine the results to show the numerical elements of
C
.
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General Contents
Detailed Contents
Index