Math 205 A B Quiz 03 Vector Worksheet - Bates College - 2012
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1Quiz 03 page 1
09/28/2012
Math 205 A B
Name
0 2
2
4
2
4
1 0 0
3 0
1
1 6
3
9
2
3
0 1 0
2 0
0
Let A =
2 3
4 12
3
8
; then rref(A)=
0 0 1
0 0
0
3 6
0
3
1
5
0 0 0
0 1
2
1 2
1
1
1
3
0 0 0
0 0
0
Let S = {a
, a
, . . . , a
} be the set of column vectors of A.
1
2
6
1. Write all solutions of Ax = 0 in parametric vector form:
2. It’s clear that S is LD. Which vectors in S can be expressed as linear combinations (LC’s) of the other vectors?
Don’t write the vectors out; use their names (a
, etc.) in a simple list instead.
, a
1
2
3. If a
can be written as a LC of the other vectors, find a way to do it using as few of the other vectors as possible.
2
Otherwise, explain correctly why a
is not a LC of the other vectors.
2
4. If a
can be written as a LC of the other vectors, find a way to do it using as few of the other vectors as possible.
3
Otherwise, explain correctly why a
is not a LC of the other vectors.
3
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