13x+5y-3z+w=18
2x+12y+z-4w=13
3x-4y+10z+w=29
2x+y-32z+9w=31
|
n (iteration)
|
x
|
y
|
z
|
w
|
|
0
|
0
|
0
|
0
|
0
|
|
1
|
18/13
|
133/156
|
551/195
|
13.09
|
|
2
|
3203/4563
|
17217/3380
|
3.4181
|
14.8756
|
|
3
|
-0.93
|
5.912
|
4.05626
|
17.4165
|
|
4
|
-1.2929
|
6.7663
|
4.25274
|
18.101
|
|
5
|
-1.6288
|
7.034
|
4.39215
|
18.641
|
|
6
|
-1.7411
|
7.2213
|
4.44673
|
18.84
|
|
7
|
-1.8158
|
7.2953
|
4.4789
|
18.9624
|
|
8
|
-1.8463
|
7.3386
|
4.4931
|
19.0148
|
|
9
|
-1.8637
|
7.3578
|
4.501
|
19.0438
|
13x₁=18-0=18, x₁=18/13,
12y₁=13-2x₁+0=13-36/13=133/13, y₁=133/156,
10z₁=29-3x₁+4y₁-0=29-54/13+133/39=1102/39, z₁=551/195,
9w=31-2x₁-y₁+32z₁=31-36/13-133/156+17632/195=117.80, w₁=13.09.
The above table shows the results up to iteration 9. Rounding to 2 decimal places we get x=-1.86, y=7.36, z=4.50, w=19.04.
Actual answers are:
x=-18002/9577, y=70658/9577, z=43173/9577, w=182641/9577.
Eventually after sufficient iterations these answers would be reached (or approximated).