Linear Algebra
MAS4105
3247
PracticeA
Prof. JLF King
23Aug2011
Welcome:
This is a practice prereq exam.
We’ll have
the actual prereq exam
(
which will be shorter
)
, in class, on
Wedn, 25Aug2010
.
Please bring linedpaper for the short induction proof.
The prereq counts only
4%
–
8%
of the course grade. It’s
purposeisforyouto
selfevaluate
ifyouhavetheprerequisite
knowledge for the Theoretical Linear Algebra course.
If
you’ve forgotten a little, that’s fine, but if you are shaky on
a
lot
of material, then you should consider using this semester
to review, and taking the Theoretical course in Spring.
A1:
On your own sheets of paper, please write (
double
spaced
) proofs of the following, in complete English sen
tences.
Do
not
restate the problem.
Bin1
Define binary operation “
♥
”, on pair of reals, by
x
♥
y
:=
xy
+
y
. Prove or disprove (
i.e give an explicit coun
terexample
): “
♥
” is associative.
On the set of postive real numbers, define “
F
”, a binary
operation, by
a
F
b
:=
a
log(
b
)
. Prove or disprove: “
F
” is
associative.
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 Fall '09
 RUDYAK
 Addition, Vector Space, Mathematical Induction, Quadratic equation

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