MATH 220 Final: Math 220 M220-Fall01-Final-Answers
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MATH 220 FINAL EXAMINATION IDecember
13,
20011
Name
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c
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ID Section #
__
_
There are ??multiple choice questions. Each problem
is
worth 5 points. Four possible answers
are given for each problem, only one of which
is
correct. When you solve a problem, note
the letter next to the answer
that
you wish to
give
and blacken the corresponding space on
the answer sheet. Mark only one choice; darken the circle completely (you should not be
able to see the letter after you have darkened the circle).
THE USE
OF
CALCULATORS DURING THE EXAMINATION
IS
FORBIDDEN.
CHECK THE EXAMINATION BOOKLET BEFORE
YOU START. THERE SHOULD BE
??
PROBLEMS
ON ?? PAGES (INCLUDING THIS ONE).
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MATH 220 FINAL EXAMINATION PAGE 2
1.
What
is
~umLiUli
of following system of equations
@
Xl
b)
Xl
c)
Xl
d)
Xl
Xl
+
2X2
+ X3 1
-2XI
+
X2
-
2X3
3
-Xl
+
3X2
-X3 4?
=
-1-
X3,X2
=
l,x3
is free.
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1'0.)
Q
IS
{)
~
l'
L ,
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rk 1 1 J
= 1 +
X2,X2
is free,x3
=-1.
_\
-0
-\
4
tV
S 0 5
=
-X2
+
X3,
and
X2,
X3 are free.
[~~
I -
IJ
=
2X2
X3,
and X2) X3 are free. N
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j
rJ
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2 Q \ J o a
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0
o 0 Cl 0
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2.
Which of the following matrices
is
in echelon form (but not necessarily reduced echelon
form)?
1
o 3
2]
a)
b)
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[~
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i]
1 0
d) 0 2
[
O~
--
MATH 220 FINAL EXAMINATION PAGE 3
3.
What
geometric figure mformed from
the
span of the vectors m'
H]
,
[i!]
?
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A L
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1.
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to
d)
all of
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4.
Which of the following sets of vectors
span
1R
3?
c=
w],
m, m,
[m
A=W],
m,
[!]}
a) A only
we
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b) B only
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c)
A and B
@ A
and
C
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