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Math 294
Prelim 1
Spring 2005
Do ALL
5 problems.
Justify all your answers.
Points will be deducted for illegible
writing.
No calculators.
No points will be awarded for unexplained answers
.
1a Consider a matrix A of the form
ab
A
ba
=
−
, where
22
1
+
=
.
Find two
nonzero perpendicular vectors
v
G
and
w
G
such that
A
vv
=
G
G
and
A
ww
= −
G
G
.
(20pts)
1b Without doing
any calculations
, find
1
A
−
.
Explain your reasoning.
(5pts)
2a Decide whether the linear transformation
yA
x
=
G
G
defined by
1123
21
2
3
31
2
3
23
49
yxxx
yx
x
x
x
x
=++
=+ +
is invertible.
Find the inverse transformation
1
A
−
if it exist.
(15pts)
2b An
n
by
n
square matrix
B
has two equal columns, is it invertible ?
(
no credit
will be given to a right answer but wrong reasoning; if any part of your reasoning is
wrong, it is a wrong reasoning
)
(
5
p
t
s
)
3a
Find the set
S
of all vectors that are perpendicular to
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This note was uploaded on 04/04/2008 for the course MATH 2940 taught by Professor Hui during the Spring '05 term at Cornell University (Engineering School).
 Spring '05
 HUI
 Math, Linear Algebra, Algebra

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