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Math 20F
Midterm Exam 2 Solutions
May 21, 2008
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10
2
8
3
10
4
12
Σ
40
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1. Consider the following elementary row operations on the set of 3
×
3 matrices:
(1) Add 3 times the first row to the third row
(2) Interchange the second and third rows
(3) Multiply the first row by 7.
Let
E
1
,
E
2
, and
E
3
be the corresponding elementary matrices.
a. Write down all the matrices
E
1
,
E
2
,
E
3
,
E
−
1
1
,
E
−
1
2
, and
E
−
1
3
.
Solution:
E
1
=
1
0
0
0
1
0
3
0
1
,
E
2
=
1
0
0
0
0
1
0
1
0
,
E
3
=
7
0
0
0
1
0
0
0
1
,
E
−
1
1
=
1
0
0
0
1
0

3
0
1
,
E
−
1
2
=
1
0
0
0
0
1
0
1
0
,
E
−
1
3
=
1
/
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 Spring '09
 Chan
 Math, Linear Algebra, Algebra, E3 E2 E1, corresponding linear transformation

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