expressed as a product of two triangular matrices,
one lower and another upper thus
A=LU
where
111213
21222321
3132333132
111213
2223
33
100
;10
1
0
00
aaa
AaaaLl
aaall
uuu
Uuu
u
⎡⎤⎡⎤
⎢⎥⎢⎥
==
⎢⎥⎢⎥
⎢⎥⎢⎥
⎣⎦⎣⎦
⎡⎤
⎢⎥
=
⎢⎥
⎢⎥
⎣⎦
Proof A=LU
111213
212223
313233
111213
2111211222211223
3111311232223113322333
aaa
aaa
aaa
uuu
luluuluu
lululululuu
⎡⎤
⎢⎥
⇒
⎢⎥
⎢⎥
⎣⎦
⎡⎤
⎢⎥
=++
⎢⎥
⎢⎥
+++
⎣⎦
We have nine equations in nine unknowns which can
be solved for. Indeed we ha
ve
13
21
31
3
31
3
211100
[]
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