MATH 461 – Summer I 2006 – Exam 1
JUSTIFY ALL ANSWERS and SHOW ALL WORK
CALCULATORS ARE NOT
ALLOWED
Put a BOX around your ﬁnal answer to each part. No calculators allowed. You must be careful on arithmetic
– check. No proof is needed for TRUEFALSE questions; just write clearly. A statement is TRUE if it is
true without exception. You may assume given matrix equations are well deﬁned (i.e. the matrix sizes are
compatible). x
1. (10 pts) Find all solutions for the following system of equations:
11
x
1
+ 22
x
2
+ 27
x
3

16
x
4
= 17

3
x
1

6
x
2

6
x
3
+ 9
x
4
= 12
2
x
1
+ 4
x
2
+ 5
x
3

3
x
4
= 3
2. (24 pts) For each of the following, answer TRUE or FALSE.
(a) For two
n
×
n
matrices
A
and
B
, (
AB
)
T
=
A
T
B
T
.
(b) If
U
and
A
are
n
×
n
matrices, then the equations
UAx
= 0 and
Ax
= 0 have the
same solution set.
(c) If
E
is an elementary matrix and
b
is a vector, then the equations
EAx
=
b
and
Ax
=
E

1
b
have the same solution set.
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 Spring '08
 Jake
 Math, Linear Algebra, pts, ax

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