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MATH 2311 MIDTERM # 1
FALL SEMESTER 2 007
Lance L. Littlejohn
Name __ =~~O~L~ur~~I~OllN~SL' ________ __
Instructions: Show all work. Partial credit can only be given if sufficient work accompa
nies each answer. Calculators may be used but exact answers are required. This examination
is out of 50 points. GOOD LUCK'
Problem No. Points
1.
2.
3.
4.
5.
6.
Grade
/50
1. (5 P OINTS) Express (3, 1,2) as a linear combination of t he vectors (1, 0,0), (1 , 1, 0),
and (1, 1, 1).
(~
I
3
"~l+i?J
0
2
I
I
"r
I
0
J
2
~3+1<~ (I 0
0 2
=) 01
0
/
o 0
;;L

 
2. (9 POINTS)
(a) ( 3 Points) Row reduce the following matrix A into rowreduced echelon form:
'2
o
<9
c \
\ 1
o 0
(
2 4 5 3)
A = 3 6 7 4 .
5 10 11 6
'2 2
/
o I
o I
1)
1
Q
(b) (4 POINTS) Find a pammetric form of all solutions to the system
 0

)(., to:, \, OI.~I "
Aj,t : {f ........
2x + 4y  5z + 3t
3x+6y7z+4t
5x + lOy  11 z +...
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