MATH 223, Linear Algebra
Fall, 2010
Assignment 4, due
in class
Monday, October 4, 2010
1. Find a basis for each of the row space, column space and null space of the
following matrix
A
over the complex numbers. What is its rank? Express
each row of
A
as a linear combination of the rows in your basis for the
row space; express each of the columns of
A
as a linear combination of the
vectors in your basis for the column space.
A
=
1
2
i
2 + 4
i
1 + 8
i
4 + 14
i
1

i
3 + 2
i
7 +
i
12 + 7
i
23 + 9
i
i
0

2

2 +
i

3 + 2
i
4

1 +
i
10
i
1 + 11
i
4 + 22
i
.
2. Let
V
=
Z
4
2
and
W
1
=
Span
1
0
1
0
,
0
1
0
1
and
W
2
=
Span
0
1
1
0
,
1
0
0
1
and be subspaces of
V
. Find a basis for
W
1
+
W
2
and one for
W
1
∩
W
2
.
3. Let
V
=
C
5
and
W
1
=
Span
1
i
1
i
1
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 Spring '07
 Loveys
 Linear Algebra, Algebra, Vector Space, Complex Numbers, Linear combination

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