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Math 136
Assignment 5
Due: Wednesday, Feb 24th
1.
Let
A
=
±
12

1
3

2

1
²
,
B
=
±
1 0
0
02

3
²
,
C
=
±
5

1

²
. Determine the following
a) 2
A

B
b)
A
(
B
T
+
C
T
)
c)
BA
T
+
CA
T
2.
Prove that if
±x
∈
M
(3
,
2) and
a,b
∈
R
are scalars, then (
a
+
b
)
=
a±x
+
b±x
.
3.
Determine which of the following mappings are linear. Find the standard matrix
of each linear mapping.
a)
f
(
x
1
,x
2
3
) = (
x
1
+
x
2
+1
3
,
0).
b)
f
(
x
1
2
) = (0
1
+2
x
2
2
).
c) proj
(

2
,
1)
.
4.
Determine the standard matrix of a re±ection in
R
2
in the line
x
1

5
x
2
= 0.
5.
Let
L
and
M
be linear mappings from
R
n
to
R
m
, and let
k
∈
R
.
a) Prove that
L
+
M
and
kL
are linear mappings.
b) Prove that [
+
M
]=
k
[
L
]+[
M
].
6.
Suppose that
S
and
T
are linear mappings with matrices
[
S
4

3
11
5

3

20
[
T
±
4
0 2 3

2130
²
.
a) Determine the domain and codomain of each mapping.
b) Determine the standard matrices that represent
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This note was uploaded on 04/30/2010 for the course MATH 136 taught by Professor All during the Winter '08 term at Waterloo.
 Winter '08
 All
 Scalar

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