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MATH 2311 MIDTERM # 1
SPRING SEMESTER 2008
Lance L. Littlejohn
N~e __ ~S~O~L~U~TLIO~N~S~ ________ __
Instructions: Show all work. Partial credit can only be given if sufficient work accompa
nies each answer. This examination is out of 50 points. GOOD LUCK!
Problem No. Points
I.
2
3.
4.
5.
6.
Grade
/ 50
I. (6 POINTS) Determine if the vectors {(I, - 1, 1), (2, 1, 3) , (-1, 4,0)) arc linearly depen
dent or linearly independent. If they are linearly dependent, find a specific non-trivial
linear combination of them that is equal to the zero vector.
cl,-+L~-O~O
-d.+~+ IflS'~o
oI.+-3{l = 0
J.. -I) Q .. ,~,-~\ .;>.
1 't -> 0 3
3 0 -~1"<;(3 0 1
'is;. 01. - :, "t ::: 0
~+«_o
-I) ;''K2 ( ;:). -\)-2~~"'~1~' 0 -3)
:3 --> 0 \ I _? -~2 0 \ \
\ 0 \ I .. ''"3 0 0 0
(Nc-+e , d, ~.: \,~~.¥.:-VO.k.,. '0=\ >cr oJ.~ 3 ~ p=-I
'tJi~ this cho \ee,
5(1,-1, 1)-('2,\,0+(-\,'t.o)~ (0,/),0).
~-------= _. ----
-~,--
2. (a) ( 4 POINTS) P...

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