Math 152, Spring 2010
Assignment #7
Notes:
•
Each question is worth 5 marks.
•
Due in class: Monday, March 8 for MWF sections; Tuesday, March 9
for TTh sections.
•
Solutions will be posted Tuesday, March 9 in the afternoon.
•
No late assignments will be accepted.
1. Let
T
and
S
denote the linear transformations of
R
2
which reﬂect
vectors in the
x
axis, and rotate vectors by 30 degrees clockwise.
(a)
Find matrices representing
S
and
T
.
(b)
Find matrices representing
ST
and
TS
.
2. Suppose
T
is a linear transformation from
R
2
to
R
3
, given by the
matrix
1 1
1 0
0 2
.
If
L
is a line in
R
2
, passing through the point (1
,
1) and in the direction
of the vector
~v
= (1
,
2
,
1), then ﬁnd the image of the line
L
under
T
.
(Note: the vectors in this problem and the problem below have been
written as row vectors to save space.)
3. Suppose
T
is a linear transformation from
R
3
to
R
3
such that
T
(
e
1
) =
(1
,
1
,
1),
T
(
e
2
) = (1
,
2
,
1), and
T
(
e
3
) = (1
,
0
,
1).
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 Spring '08
 Caddmen
 Math, Linear Algebra, Vector Space, Alberta, linear transformation

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