Math 205 A & B Quiz 03 Worksheet - Bates College, 2015
ADVERTISEMENT
1Math 205 A & B
Quiz 03 ver01 page 1
02/13/2015
Name
On this quiz, show any RREF’d matrices you use in any given problem.
7 9 8
5
5
2 1 7
4
1. Let A =
. Define T : R
by T (v) = Av for any v ∈ R
. Let m =
8
and s =
p
→ R
a
p
1 1 2
3
3
5 7 4
2
1a. What are the values of p and a? (Label which is which)
1b. Find both T (m) and T (s). If one of them is not possible to find, explain why. Label your answers.
20
10
1c. Find all x for which T (x) =
.
0
20
13
13
1e. Today is Friday the 13th, so the vector u =
is extremely unlucky. Explain why u is not in the image of T .
13
13
2. Suppose that T is a transformation from R
to R
. There are two conditions that T must satisfy in order to be a
n
m
linear transformation. They are:
2a. the equation
is true for every pair of vectors u and v in R
, and
n
2b. the equation
is true for any scalar α ∈ R and vector w ∈ R
.
n
s
st
2
2
2c. Define T : R
by T
=
. Show that T fails to satisfy the equation in (2a) using the
→ R
3s + 2t + 6
t
8
4
vectors u =
and v =
.
7
5
ADVERTISEMENT
0 votes
Related Articles
Related forms
Related Categories
Parent category: Education