Math 1b — Final Review Questions
Due 3:00pm, Monday, March 9, 2009
We will discuss some of these topics on the review session Wednesday. You don’t
have to do all these problems; just look them over. You can also raise other topics and
questions. We won’t have time to talk about everything, though.
1.
Use the method of the proof of Theorem 1 in the notes on isometries to write the
rotation
Q
=
±
ab
−
ba
²
(here
a
2
+
b
2
= 1) as the product of two reFections. There will be many solutions. To
ensure that we all get the same answer, take
z
=[1
,
0]
>
.
2.
Here is an LP problem: Maximize 7
x
−
3
y
+
z
subject to
(
x
+
y
−
z
=7
2
x
+3
y
−
4
z
≤
20
x
≤
0
,y
≥
0
,z
≥
0
(i) Convert this to an LP problem in Standard ±orm. Give
A
,
b
,
c
.
(ii) Convert this to an LP problem in Dual Standard ±orm. Give
A
,
b
,
c
.
(iii) Convert this to an LP problem in Canonical ±orm. Give
A
,
b
,
c
.
(iv) Convert this to an LP problem in Dual Canonical ±orm. Give
A
,
b
,
c
.
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 Winter '09
 Bopanna
 Math, Linear Algebra, Vector Space, Singular value decomposition, Orthogonal matrix

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