Assignment #7 - Stephanie Campbell due 11/21/2010 at...

Stephanie Campbell Assignment 7 MATH133, Fall 2009
due 11/21/2010 at 11:59pm EST.
You may attempt any problem an unlimited number of times.
1. (1 pt)
Which of the following transformations are linear?
2. (1 pt) Find the matrix M of the linear transformation
- 5 x
1
+ 7 x
2
8 x
1
+ x
2
.
M = .
3. (1 pt) If T : R
2
→ R
2
is a linear transformation such that
T
1
0
=
-4
5
and T
0
1
=
10
-9
,
then the standard matrix of T is A = .
4. (1 pt) If T : R
3
→ R
3
is a linear transformation such that
T


1
0
0


=


4
1
4


, T


0
1
0


=


-4
-2
-1


,
and T


0
0
1


=


4
2
2


,
then T


-1
-2
0


=




.
5. (1 pt) Find the matrix M of the linear transformation


x
1


=
4 x
1
+ x
2
+ 8 x
3
T : R
3
→ R
2
given by T x
2
x
3
- 2 x
1
+ 5 x
3
.
M = .