Math 205 A & B Quiz 02 Ver01 Worksheet - Bates College, 2014
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1Math 205 A & B
Quiz 02 ver01 page 1
01/24/2014
Name
1
2
0
0
1. Let a
=
and a
=
.
1
2
3
1
3
1A) Find a vector b ∈ R
different from both a
and a
that is in Span{a
} and explain how you found b.
, a
1
2
1
2
3
1B) Find a vector d ∈ R
that is obviously not in Span{a
} and explain why d is not in that span.
, a
1
2
4
8
5
1
22
8
2
4
5
7
16
11
2. Let c
=
, c
=
, c
=
, and c
=
. Also, let v =
and w =
.
1
2
3
4
0
0
2
6
4
7
1
2
2
2
7
4
2A: Determine if v a linear combination of c
, c
, c
, and c
, and if it is, find all possible solutions of the vector equation
1
2
3
4
+ · · · + x
= v. Express your values of the x
’s in the agreed-upon format. Show any RREF matrices used in your
c
c
x
1
1
4
4
i
solution.
2B: Explain whether w is in the Span of {c
}. Again show any RREF matrices used in your explanation.
, c
, c
, c
1
2
3
4
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