Math 330 Chapter 3 Quizzes
Section 3.1  Take home assigned February 18, 2009
Suppose that
A
and the product
AB
are as given below. Determine
B
A
=
bracketleftBigg
1

1
3
0
bracketrightBigg
AB
=
bracketleftBigg
2

2
0
0
6
0
0
1
bracketrightBigg
SOLUTION:
Since
A
is 2
×
2 and
AB
is 2
×
4 it must mean that
B
is 2
×
4. The 4 columns of
AB
come from
come from linear combinations of the columns of
A
. Each column of
B
gives weights to produce
the resulting column of
AB
.
Let
vectora
1
and
vectora
2
denote the first and second columns respectively of
A
. Then we note the following
about the columns
vector
c
1
,vector
c
2
,vector
c
3
,
and
vector
c
4
of
AB
:
•
By inspection
vector
c
1
= 2
vectora
1
+ 0
vectora
2
.
•
By inspection
vector
c
2
= 0
vectora
1
+ 2
vectora
2
•
By inspection
vector
0 =
vector
c
3
= 0
vectora
1
+ 0
vectora
2
•
We can find the last column
vectorx
of
B
by solving the system
Avectorx
=
vector
c
4
:
bracketleftBigg
1

1
3
0
bracketrightBigg bracketleftBigg
b
14
b
24
bracketrightBigg
=
bracketleftBigg
0
1
bracketrightBigg
=
⇒
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 Spring '08
 Johnson,J
 Math, Linear Algebra, Algebra, Following, Column

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