This preview shows page 1. Sign up to view the full content.
14. Suppose that (
α
1
,...,α
n
) and (
β
1
,...,β
n
) are solutions of the system
of linear equations
n
X
j
=1
a
ij
x
j
=
b
i
,
1
≤
i
≤
m.
Then
n
X
j
=1
a
ij
α
j
=
b
i
and
n
X
j
=1
a
ij
β
j
=
b
i
for 1
≤
i
≤
m
.
Let
γ
i
= (1

t
)
α
i
+
tβ
i
for 1
≤
i
≤
m
. Then (
γ
1
,...,γ
n
) is a solution of
the given system. For
n
X
j
=1
a
ij
γ
j
=
n
X
j
=1
a
ij
{
(1

t
)
α
j
+
tβ
j
}
=
n
X
j
=1
a
ij
(1

t
)
α
j
+
n
X
j
=1
a
ij
tβ
j
=
(1

t
)
b
i
+
tb
i
=
b
i
.
15. Suppose that (
α
1
,...,α
n
) is a solution of the system of linear equations
n
X
j
=1
a
ij
x
j
=
b
i
,
1
≤
i
≤
m.
(1)
Then the system can be rewritten as
n
X
j
=1
a
ij
x
j
=
n
X
j
=1
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 12/19/2011 for the course MAS 3105 taught by Professor Dreibelbis during the Fall '10 term at UNF.
 Fall '10
 Dreibelbis

Click to edit the document details