Ans.
| 20 |
-2 |
4 |
= |
1 |
0 |
0 |
* |
U11 |
U12 |
U13 |
| -1 |
-10 |
1 |
121 |
1 |
0 |
0 |
U22 |
U23 |
| 2 |
3 |
20 |
131 |
132 |
1 |
0 |
0 |
U33 |
| |
= |
U11 |
U12 |
U13 |
| L21U11 l21U12+U22 l21 |
U13+U23 |
| L31U11 l31U12+l32U22 l31U13+l32U23+U33 |
Comparing on both sides, we get
U11=20
U12=-2
U13=4
L21U11=-1
L21 = -1/20
L21U12+U22=-10
U22= -101/10
L21U13+U23=1
U23=6/5
L31U11=2
L31=1/10
L31U12+L32U22=3
L32= -32/101
L31U13+L32U23+U33=20
U33=2018/101
| L = |
1
-1/20
1/10
|
0
1
-32/101 1 |
0
0 |
| 20 |
2 |
4 |
| U = |
0 |
-101/10 6/5 |
|
| 0 |
0 |
2018/101 |
| Ly=b |
| L |
* |
(Y1) |
= |
(8) |
| (Y1) |
(-3) |
| (Y1) |
(7) |
By solving the above eqn, we get
Y1=8
Y2=-13/5
Y3=5.38
Now Ux = y
| U |
* |
X1 |
8 |
| X2 |
-13/5 |
| X3 |
5.38 |
By solving the above eqn, we get
X1 =0.4247 (approx)
X2=0.289386138(approx)
X3=0.269066402(approx)