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Newberger Math 247 Spring 03
Quiz 2.12.3
name:
1.
Find the inverse of
A
=
1 0 0
5 1 0
0 2 2
.
1 0 0
1 0 0
5 1 0
0 1 0
0 2 2
0 0 1
∼
1 0 0
1 0 0
0 1 0

5 1 0
0 2 2
0 0 1
∼
1 0 0
1
0 0
0 1 0

5
1 0
0 0 2

10

2 1
Thus
A

1
=
1
0 0

5
1 0

5

1
1
2
.
2.
Suppose
A
is invertible and
AB
=
0
, where
0
denotes the zero matrix.
Show that
B
=
0
.
Since
A
is invertible, we have the matrix
A

1
to work with. Multiplying
AB
=
0
by
A

1
, we get
A

1
(
AB
) =
A

1
0
. Using the associative law, this
becomes
(
A

1
A
)
B
=
A

1
0
. But
A

1
A
=
I
and the right hand side is
0
,
so we get
B
=
0
.
3.
Suppose
B
=
PAP

1
, where
A
and
P
are invertible
n
×
n
matrices. Find
B

1
.
The inverse of the product of invertible matrices is the product of the
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This note was uploaded on 01/12/2010 for the course MATH 247 taught by Professor F,newberger during the Spring '03 term at Stanford.
 Spring '03
 F,newberger
 Math

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