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Math 110—Linear Algebra
Fall 2009, Haiman
Problem Set 8
Due Monday, Oct. 26 at the beginning of lecture.
1. For each of the following statements, either prove that it is true for all systems of
m
linear equations in
n
unknowns, or give a counterexample.
(a) If the system has a unique solution, then
m
≥
n
.
(b) If
m
≥
n
and the system is consistent, then the solution is unique.
(c) Given a ﬁxed coeﬃcient matrix
A
, if the system
Ax
=
b
is consistent for every
b
, then
m
≤
n
.
(d) If
m
≤
n
, then the system is consistent.
2. Use Gaussian elimination to ﬁnd all solutions to each of the following systems of linear
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Unformatted text preview: equations: (a) 31 0 325 3 22 11 1 3 2 22 4 9 1 x 1 x 2 x 3 x 4 x 5 = 8 64 11 (b) 31 0 325 3 22 11 1 3 2 22 4 9 1 x 1 x 2 x 3 x 4 x 5 = 1211613 3. Section 3.4, Exercise 5...
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This note was uploaded on 08/16/2010 for the course MATH 110 taught by Professor Gurevitch during the Fall '08 term at University of California, Berkeley.
 Fall '08
 GUREVITCH
 Linear Algebra, Algebra, Linear Equations, Equations

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