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Math 136
Assignment 8
Due: Wednesday, Mar 24th
1.
For each of the following matrices, ±nd the inverse, or show that the matrix is not invertible.
a)
A
=
1

12
315
223
.
b)
B
=
1

102
0
1
1 0
2

235
1
0
1 3
.
2.
Let
B
=
2

11
0
1
1
1

1

1
. Find
B

1
and use it to solve
B±x
=
±
d
, where
±
d
= (4
,

2
,
3).
3.
a) Prove that if
A
and
B
are
n
×
n
matrices such that
AB
is invertible, then
A
and
B
are invertible.
b) Give an example of 2
×
3 matrix
A
, and 3
×
2 matrix
B
such that
AB
is invertible.
Are
A
and
B
invertible?
4.
Write the 4
×
4 elementary matrices that correspond to each of the following
elementary row operations.
a) add 2 times the third row to the second.
b) interchange the ±rst row and the fourth row.
c) multiply the second row by 3.
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This note was uploaded on 04/30/2010 for the course MATH 136 taught by Professor All during the Winter '08 term at Waterloo.
 Winter '08
 All
 Matrices

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