Graphics Programs Reference
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=
10.Solve the equations
AX
B
by Doolittle's decompositionmethod, where
⎡
⎣
⎤
⎦
⎡
⎣
⎤
⎦
4
−
3
6
1 0
0 1
00
A
=
B
=
8
−
3 0
−
4
12
−
10
11. Solve the equations
Ax
=
b
by Choleski's decompositionmethod, where
⎡
⎣
⎤
⎦
⎡
⎣
⎤
⎦
111
122
123
1
A
=
b
=
3
/
2
3
12. Solve the equations
⎡
⎣
⎤
⎦
⎡
⎣
⎤
⎦
=
⎡
⎣
⎤
⎦
4
−
2
−
3
x
1
x
2
x
3
1
.
1
0
12
4
−
10
−
16
28
18
−
2
.
3
by Doolittle's decompositionmethod.
13. Determine
L
that results fromCholeski's decomposition of the diagonal matrix
⎡
⎣
⎤
⎦
α
1
00
···
0
α
2
0
···
A
=
α
3
···
00
.
.
.
.
.
.
14.
Modify the function
gauss
so that it will work with
m
constant vectors. Test the
program by solving
AX
=
B
, where
⎡
⎣
⎤
⎦
⎡
⎣
⎤
⎦
2
−
1
0
1 00
0 1 0
001
A
=
−
−
B
=
12
1
0
−
11
15.
Awell-known example of an ill-conditionedmatrix is the
Hilbert matrix
⎡
⎣
⎤
⎦
11
/
21
/
3
···
1
/
21
/
31
/
4
···
=
A
1
/
31
/
4 1
/
5
···
.
.
.
.
.
.
Write aprogram thatspecializes in solving the equations
Ax
b
by Doolittle's
decompositionmethod, where
A
is the Hilbert matrix of arbitrary size
n
=
×
n
, and
n
b
i
=
A
i j
j
=
1
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