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18.06
Quiz
1
March
1,
2010
Professor
Strang
Your
PRINTED
name
is:
1.
Your
recitation
number
or
instructor
is
2.
3.
4.
1.
Forward
elimination
changes
A
x
=
b
to
a
row
reduced
R
x
=
d
:
the
complete
solution
is
⎤
⎡
⎤
⎡
⎤
⎡
4
2
5
x
=
⎢
⎢
⎢
⎣
⎥
⎥
⎥
⎦
+
c
1
⎢
⎢
⎢
⎣
⎥
⎥
⎥
⎦
+
c
2
⎢
⎢
⎢
⎣
⎥
⎥
⎥
⎦
0
1
0
0
0
1
(a)
(14
points)
What
is
the
3
by
3
reduced
row
echelon
matrix
R
and
what
is
d
?
Solution:
First,
since
R
is
in
reduced
row
echelon
form,
we
must
have
±
T
d
=
4
0
0
The
other
two
vectors
provide
special
solutions
for
R
,
showing
that
R
has
rank
1:
again,
since
it
is
in
reduced
row
echelon
form,
the
bottom
two
rows
must
be
all
0,
and
⎡
⎤
R
=
±
T
the
top
row
is
1
−
2
−
5
,
i.e.
⎢
⎢
⎢
⎣
1
0
−
2
0
−
5
0
⎥
⎥
⎥
⎦
.
0
0
0
(b)
(10
points)
If
the
process
of
elimination
subtracted
3
times
row
1
from
row
2
and
then
5
times
row
1
from
row
3,
what
matrix
connects
R
and
d
to
the
original
A
and
b
?
Use
this
matrix
to
±nd
A
and
b
.
Solution:
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 Fall '10
 Strang
 Linear Algebra, Algebra

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