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CO350
Assignment 1
Due: May 14 at 2pm.
Submit your assignment in drop box 2 (opposite MC4066) by 2pm. Your full name, stu
dent ID number, the course number, and the name of your instructor should all be clearly
visible on the front of your assignment. You may discuss the assignment questions with
other students, but you must write your solutions up independently, and all submitted
work must be your own.
Exercise 1:
(linear algebra review.) Let
A
∈
R
m
×
n
and
b
∈
R
m
.
(a)
Show that, if the system
Ax
=
b
has a solution and the columns of
A
are not linearly
independent, then
Ax
=
b
has inﬁnitely many solutions.
(b)
Show that, if the system
Ax
=
b
has a solution and the columns of
A
are linearly
independent, then
Ax
=
b
has a unique solution.
Exercise 2:
(linear programming) Let
A
∈
R
m
×
n
,
b
∈
R
m
, and let
c
∈
R
n
. Show that,
if max(
c
t
x
:
Ax
=
b, x
≥
0) has two solutions, then it has inﬁnitely many solutions.
Exercise 3:
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This note was uploaded on 05/28/2011 for the course CO 350 taught by Professor S.furino,b.guenin during the Fall '07 term at Waterloo.
 Fall '07
 S.Furino,B.Guenin

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