Math 205a Quiz 04 Worksheet - 2008
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1Math 205A
Quiz 04 page 1
February 8, 2008
NAME
n
m
1. Suppose T : R
→ R
is a transformation. What are the two defining properties that T must satisfy
in order to be a linear transformation?
4
2
1
0
and T
.
2. Suppose that T
=
3
=
5
0
1
1
8
2A. Find the (standard) matrix for T .
2
2B. Find T
.
5
2
10
7
3
3
3. Suppose T : R
→ R
has (standard) matrix A =
1
5
6
2
10
15
3
3A. What, if any, conditions does a vector b ∈ R
need to satisfy in order to be in the image of T ?
Show any RREF matrices you use in finding your answer.
15
does indeed satisfy the answer to 3A.
5
3B. Show that b =
25
15
.
3
3C. Find just one x ∈ R
such that T (x) =
5
25
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