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?
•
A.
y
1
=
9
x
1
+
x
2
y
2
=
-
x
1
•
B.
y
1
=
x
2
2
y
2
=
x
3
y
3
=
x
1
•
C.
y
1
=
0
y
2
=
7
x
2
•
D.
y
1
=
8
x
2
y
2
=
-
3
x
3
y
3
=
-
6
x
1
•
E.
y
1
=
x
1
+
2
y
2
=
x
2
•
F.
y
1
=
9
y
2
=
7
y
3
=
8
2.
(1 pt) Find the matrix
M
of the linear transformation
T
:
R
2
→
R
2
given by
T
x
1
x
2
=
-
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
T
:
R
3
→
R
2
given by
T
x
1
x
2
x
3
=
4
x
1
+
x
2
+
8
x
3
-
2
x
1
+
5
x
3
.
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- Fall '08
- KLEMES
- Math, Linear Algebra, Transformations, Vector Space, Euclidean geometry, Linear map, linear transformation
-
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