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=
,
2.
Use Doolittle's decomposition to solve
Ax
b
where
⎡
⎣
⎤
⎦
⎡
⎣
⎤
⎦
4 8 0
813 16
20 16
24
18
A
=
b
=
−
−
91
119
3. Determine
L
and
D
that result fromDoolittle's decomposition of the matrix
⎡
⎣
⎤
⎦
2
−
2
000
−
25
−
6
00
A
=
0
6 6 2 0
0012
−
39
−
6
000
−
6 4
4.Solve the tridiagonalequations
Ax
=
b
by Doolittle's decompositionmethod,
where
⎡
⎣
⎤
⎦
⎡
⎣
⎤
⎦
6200
0
2
−
17200
0
−
3
4
A
=
282 0
0037
−
b
=
2
00035
−
−
3
1
5.
Use Gauss eliminationwith scaledrow pivoting to solve
⎡
⎣
⎤
⎦
⎡
⎣
⎤
⎦
=
⎡
⎣
⎤
⎦
4
−
21
x
1
x
2
x
3
2
−
21
−
1
−
1
0
−
236
6. Solve
Ax
=
b
by Gauss eliminationwith scaledrow pivoting, where
⎡
⎣
⎤
⎦
⎡
⎣
⎤
⎦
2
.
34
−
4
.
10
1
.
78
0
.
02
A
=
−
1
.
98
3
.
47
−
2
.
22
b
=
−
0
.
73
2
.
36
−
15
.
17
6
.
81
−
6
.
63
7. Solve the equations
⎡
⎣
⎤
⎦
⎡
⎣
⎤
⎦
=
⎡
⎣
⎤
⎦
2
−
1
00
x
1
x
2
x
3
x
4
1
0
0
0
00
−
11
0
−
12
−
1
−
−
12
1
0
by Gauss eliminationwith scaledrow pivoting.
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