Math 205a Quiz 01 Worksheet - Bates College, 2007
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1
2Math 205A
Quiz 01, page 1
September 14, 2007
NAME
1
2
6
1
2
3
9
3
1. Suppose u
=
, u
=
, u
=
, and u
=
.
1
2
3
4
5
13
39
3
4
8
24
2
1A. What is the (initial, non-row reduced) augmented matrix which corresponds to the system
15
31
of equations you need to solve in order to find out if the vector b =
in the span of the
77
50
vectors u
, u
, u
, and u
?
1
2
3
4
1B. An augmented matrix which is row equivalent to the correct answer to (1A) is given below;
you do not need to verify this. Use it to determine if b is indeed in the span of u
, u
, u
, and u
.
1
2
3
4
If b is not in the span, explain why not. If it is in the span, find all the linear combinations of u
,
1
u
, u
, and u
which add up to b (that is, find the solution of the system of equations refered to in
2
3
4
(1A); if there are any solutions write them in terms of the free variables (if there are any)).
1 0 0 0
2
0 1 3 0
4
Row equivalent matrix:
.
0 0 0 1
5
0 0 0 0
0
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