Friday January 9
−
Lecture 3 :
Solutions to systems. Homogeneous systems.
(Refers to
section 2.2 )
Expectations:
•
Define
consistent
and
inconsistent
system.
•
Define homogeneous system.
•
Define trivial solution of a homogeneous system.
•
Show that if the number of equations equals the number of unknowns in a
homogeneous system and its RREF has no rows of zeros, i.e. RREF of the
coefficient matrix equals
I
n
then the system has only the trivial solution.
3.1
From the examples given on the handout we see that a system of linear equations
either:
o
Has no solution (case where in the last row we obtain (0 0 0
....
0 
c
) where
c
is not
zero).
In this case we refer to this system as being
inconsistent
.
o
We obtain a RREF system where all the unknowns are basic unknowns, (the solution
is unique) or
o
There are some free unknowns (we have an infinite number of solutions).
3.1.2
Note
−
If a system in not inconsistent then we say it is
consistent
.
3.2
Definition
−
Homogeneous system
. A system of the form
a
11
x
1
+
a
12
x
2
+ ... +
a
1
n
x
n
= 0.
a
21
x
1
+
a
22
x
2
+ ... +
a
2n
x
n
= 0.
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 Winter '08
 All
 Linear Algebra, Algebra, Empty set, Trivial, trivial solution

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