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Math 417 homework 4 solutions
(Given only for problems that are not straightforward computation; contact
the instructor if you still have questions about the others.)
Section 2.3 problem 4,5,20
To invert a matrix
A
, bring
h
A
.
.
.
I
n
i
to reduced row echelon form. If it is
h
I
n
.
.
.
B
i
,
then
A
is invertible and
B
=
A

1
. If you get
h
C
.
.
.
D
i
with
C
6
=
I
n
, then
A
is not invertible.
1 2 1
1 3 2
1 0 1

1
=
3
2

1
1
2
1
2
0

1
2

3
2
1
1
2
.
The matrix of problem 5 is not invertible. 4 times its ﬁrst column is the sum
of second and third column (this is a nontrivial linear relation).
The matrix of the transformation in problem 20 is
1 3
3
1 4
8
2 7 12
.
Its inverse is

8

15
12
4
6

5

1

1
1
.
1
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View Full DocumentSection 2.4 problem 18
This is always true.
(
A
2
)
·
((
A

1
)
2
) =
AAA

1
A

1
=
AIA

1
=
AA

1
=
I,
so
A
2
is invertible and (
A

1
)
2
is its inverse. It is customary to write this
shorthand as
A

2
.
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 Fall '07
 ELLING
 Math, Matrices

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