9.8
(a)
The system is first expressed as an augmented matrix:
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
−
−
−
−
−
5
.
21
5
1
1
5
.
61
2
6
3
27
1
2
10
Forward elimination:
a
21
is eliminated by multiplying row 1 by –3/10 and subtracting the result from row 2.
a
31
is
eliminated by multiplying row 1 by 1/10 and subtracting the result from row 3.
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
−
−
−
−
2
.
24
1
.
5
8
.
0
0
4
.
53
7
.
1
4
.
5
0
27
1
2
10
a
32
is eliminated by multiplying row 2 by 0.8/(–5.4) and subtracting the result from row 3.
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
−
−
−
−
1111
.
32
351852
.
5
0
0
4
.
53
7
.
1
4
.
5
0
27
1
2
10
Back substitution:
6
351852
.
5
1111
.
32
3
−
=
−
=
x
8
4
.
5
)
6
(
7
.
1
4
.
53
2
=
−
−
−
−
=
x
5
.
0
10
)
8
(
2
)
6
)(
1
(
27
1
=
−
−
−
−
=
x
(b)
Check:
5
.
21
)
6
(
5
8
5
.
0
5
.
61
)
6
(
2
)
8
(
6
)
5
.
0
(
3
27
)
6
(
)
8
(
2
)
5
.
0
(
10
−
=
−
+
+
−
=
−
+
−
−
=
−
−
+
10.2
(a)
The coefficient
a
21
is eliminated by multiplying row 1 by
f
21
= –3/10 = –0.3 and
subtracting the result from row 2.
a
31
is eliminated by multiplying row 1 by
f
31
= 1/10 = 0.1
and subtracting the result from row 3. The factors
f
21
and
f
31
can be stored in
a
21
and
a
31
.
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
−
−
−
1
.
5
8
.
0
1
.
0
7
.
1
4
.
5
3
.
0
1
2
10
a
32
is eliminated by multiplying row 2 by
f
32
= 0.8/(–5.4) = –0.14815 and subtracting the
result from row 3. The factor
f
32
can be stored in
a
32
.

This
** preview**
has intentionally

**sections.**

*blurred***to view the full version.**

*Sign up*