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Math 110 Homework 7
Partial Solutions
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3.1.4 This is a sketch of the ideas: The elementary matrix that represents
switching rows
i
and
j
is the same as the elementary matrix that repre
sents switching columns
i
and
j
. The elementary matrix that represents
multiplying row
i
by
c
6
= 0 is the same as the elementary matrix that
represents multiplying column
i
by
c
6
= 0. The elementary matrix that
represents adding
c
times row
i
to row
j
is the same as the elementary
matrix that represents adding
c
times column
j
to column
i
.
3.1.5 If
E
is elementary, then it can be obtained by performing an elemen
tary row operation to
I
n
. Then
E
t
can be obtained by performing the
corresponding column operation to
I
n
and thus is also elementary. By
the same argument, if
E
t
is an elementary matrix, so is
E
.
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 Winter '07
 Liu
 Math, Linear Algebra, Algebra

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