SOLUTION: equation using Gauss Elimination method 10x-7y+3z+5u=6 -6x+8y-z+4u=5 3x+y+4z+11u=2 5x-9y-2z+4u=7

Question 861347: equation using Gauss Elimination method
10x-7y+3z+5u=6
-6x+8y-z+4u=5
3x+y+4z+11u=2
5x-9y-2z+4u=7

Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!

Divide row1 by 10
1 -7/10 3/10 1/2 3/5
-6 8 -1 4 5
3 1 4 11 2
5 -9 -2 4 7
Add (6 * row1) to row2
1 -7/10 3/10 1/2 3/5
0 19/5 4/5 7 43/5
3 1 4 11 2
5 -9 -2 4 7
Add (-3 * row1) to row3
1 -7/10 3/10 1/2 3/5
0 19/5 4/5 7 43/5
0 31/10 31/10 19/2 1/5
5 -9 -2 4 7
Add (-5 * row1) to row4
1 -7/10 3/10 1/2 3/5
0 19/5 4/5 7 43/5
0 31/10 31/10 19/2 1/5
0 -11/2 -7/2 3/2 4
Divide row2 by 19/5
1 -7/10 3/10 1/2 3/5
0 1 4/19 35/19 43/19
0 31/10 31/10 19/2 1/5
0 -11/2 -7/2 3/2 4
Add (-31/10 * row2) to row3
1 -7/10 3/10 1/2 3/5
0 1 4/19 35/19 43/19
0 0 93/38 72/19 -259/38
0 -11/2 -7/2 3/2 4
Add (11/2 * row2) to row4
1 -7/10 3/10 1/2 3/5
0 1 4/19 35/19 43/19
0 0 93/38 72/19 -259/38
0 0 -89/38 221/19 625/38
Divide row3 by 93/38
1 -7/10 3/10 1/2 3/5
0 1 4/19 35/19 43/19
0 0 1 48/31 -259/93
0 0 -89/38 221/19 625/38
Add (89/38 * row3) to row4
1 -7/10 3/10 1/2 3/5
0 1 4/19 35/19 43/19
0 0 1 48/31 -259/93
0 0 0 473/31 923/93
Divide row4 by 473/31
1 -7/10 3/10 1/2 3/5
0 1 4/19 35/19 43/19
0 0 1 48/31 -259/93
0 0 0 1 923/1419
Add (-48/31 * row4) to row3
1 -7/10 3/10 1/2 3/5
0 1 4/19 35/19 43/19
0 0 1 0 -5381/1419
0 0 0 1 923/1419
Add (-35/19 * row4) to row2
1 -7/10 3/10 1/2 3/5
0 1 4/19 0 28712/26961
0 0 1 0 -5381/1419
0 0 0 1 923/1419
Add (-1/2 * row4) to row1
1 -7/10 3/10 0 3899/14190
0 1 4/19 0 28712/26961
0 0 1 0 -5381/1419
0 0 0 1 923/1419
Add (-4/19 * row3) to row2
1 -7/10 3/10 0 3899/14190
0 1 0 0 2644/1419
0 0 1 0 -5381/1419
0 0 0 1 923/1419
Add (-3/10 * row3) to row1
1 -7/10 0 0 911/645
0 1 0 0 2644/1419
0 0 1 0 -5381/1419
0 0 0 1 923/1419
Add (7/10 * row2) to row1
1 0 0 0 1285/473
0 1 0 0 2644/1419
0 0 1 0 -5381/1419
0 0 0 1 923/1419

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