PROBLEMS
9.1
Determine
the
number
of
total
flops
as
a
(unction
of
the
number
of
equations
ii
for
the
tridi
agonal
algorithm
Fig.
9.2
1_
se
the
eraph
teal
net
h
‘d
ti
solve
3v
=
—24
—
hv
=
34
Cheek
our
results
h
substituting
them
hack
into
the
equations.
9.3
Given
the
sy
stem
of
equations
I.
lxi
±
l(yv
=
120
—
2x
±
17.4.v
=
174
(a>
Solve
graphically
and
cheek
your
results
by
substituting
them
back
into
the
equations.
(b)
On
the
basis
of
the
graphical solution,
what
do
you
expect
regarding
the
condition
of
the
system?
(c)
Compute
the
determinant.
9.4
Given
the
system
of
equations
—
3
X2r
7
x3
=2
xi
+
2x
—
=
3
Sxi
—
2x
2
=
2
Compute
the
determinant.
Use
Cramer’s
rule
to
solve
for
the
v’s.
Use
Gauss
elimination
with
partial
pivoting
to
solve
for
the
vs.
Substitute your
results
hack
into
the
original
equations
to
check
your
solution.
Given
the
equations
0.5.vj
—
.r
=
—
9.5
l.02.v
1
—
2.
=
—15.8
(a)
Solve
graphically.
(b)
Compute
the
determinant.
(C)
On
the
basis
of
(a)
and
(b).
what
would
you
expect
regarding
the
stems
condition?
(d)
Solve
by
the
elimtnaton
of
unkttowns,
(e)
Sob.
e
again,
but
with
a
modified
slightly’
to
0.52.
Interpret
your
results.
Given
the
equations
(Jr
‘—
2x
—
=
27
3v hi’
—2s
=
(a
Sive
h\
naise
Gauss
elitutnatton.
Shos
all
steps
of
the
Ut
ii
pu
tat
ton.
b
Substitute
our
results
i
ito
the
original
equattons
to
cheek
our
ans
ers.
9.7
Gis
en
the
equations
—
hi’
—
.v =
—3x
—
7x
=
—34
(a)
Solve
by
Gauss
elimination
ss
ith
partial
pivoting.
Show
all
steps
of
the
computation.
(b)
Suhstttute your results
into
the
original
equations
to
cheek
your
answers.
9.8
Perform
the
same
calculations
as
in
Example
9.5,
hut
for
the
tridiagonal
system:
0.8
—0,4
1
.v
1
41
—0.4
0.8
—0.4
,v
=
25
L
—0.4
0.8
vi
105
9.9
Figure
P9.9
shows
three
reactors
linked
by
pipes.
As
indicated,
the
rate
of
transfer of
chemicals
through
each
pipe
is
equal
to
a
tiow
rate
(Q.
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 Spring '10
 Vorobyov
 Triangular matrix, rm inc, ted thai, Chaleskr

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