Math 205a Quiz 03 Matrix Worksheet - 2008
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1Math 205A
Quiz 03 page 1
January 25, 2008
NAME
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1. Let A =
, let c =
and let v
, v
, v
, and v
be the corresponding
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2
1
3
0
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3
2
4
1
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columns of A.
1A: Write all the solutions of Ax = c in the form p + v
where p is a particular solution of Ax = c and
h
v
represents all solutions of the corresponding homogeneous equation. Write down any RREF matrix you
h
used to help solve this problem.
1B: Find another particular solution and explain how you got it.
b
1
b
2
4
1C: Let b =
be any arbitrary vector in R
. What conditions (if any) must b
, b
, b
and b
satisfy
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2
3
4
b
3
b
4
in order for b to be in the span of v
, v
, v
, and v
? Use the method discussed in class, and again, write
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2
3
4
down any RREF matrix you used to help solve this problem.
1D: Verify that the entries of c do indeed satisfy these conditions; show your work.
4
1E: Does R
= Span{v
, v
, v
, v
}? Explain your answer.
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