18 March 2010
Teaching Assistant
Test 2
Math 1502 J Andrew
Instructions:
1.
Closed book.
2.
Show your work and explain your answers and reasoning.
3.
Calculators may be used, but are by no means necessary.
Pay particular
attention to instruction 2.
To receive credit, you must show your
work.
Unexplained answers, and answers not supported by the work
you show, will not receive credit.
4.
Express your answers in simplified form.
1.
(25)
a.
Find the matrix
R
for the reflection of
2
R
across the line
x
y

=
.
b.
Let
u
be the unit vector
=
5
4
5
3
u
.
Calculate
T
u
u
2
I
H

=
, where
I
is the 2 x 2
identity matrix.
c.
Compute
2
H
, where
H
is the matrix from part b.
d.
Find the matrix for the composition of the reflection of part a, followed by the
linear function whose matrix is
H
of part b.
2.
(25)
Determine whether or not the planes with equations listed below intersect.
If
they intersect in a point, find it.
If they intersect in a line, parametrize the line of
intersection.
25
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 Spring '08
 Morley
 Linear Algebra, Ring, Invertible matrix, Linear least squares

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