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MATH 235
Linear Algebra II
Assignment 1
Due: 9:30 am, Sept. 17/08 in the drop boxes near the tutorial centre.
1.
P
=
1
3
11
5
0

1

3

2
5
2
16

1
Q
=
1 3 1 0
2 4 1 1
4 1 1 3
R
=
1
1 +
i
5 + 3
i
1 + 2
i
i

i

i

3
i

i
0

2
i
i
The entries of matrices
P,Q,R
are taken from the ﬁelds
R
,
Z
5
,
and
C
respectively.
For
each of the above matrices
carry out the following steps:
1. Rename the initial matrix
A
, with columns
a
1
, a
2
, a
3
and
a
4
.
2. Find the unique reduced row echelon matrix
B
, with columns
b
1
,
b
2
, b
3
, b
4
3. Find a basis for nul
A
, col
A
and row
A
.
4. Is col
A
= col
B
? Why or why not?
5. Write each of
b
3
and
b
4
as a linear combination of
b
1
,
and
b
2
.
6. Write each of
a
3
and
a
4
as a linear combination of
a
1
,
and
a
2
.
7. What can you conclude from the results of steps 5) and 6)?
8. Is row
A
= row
B
? Why or why not?
9. Suppose the rows of
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 Spring '10
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 Algebra, Matrices

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