|
Question 152209: solve the system using matrices. Use Gaussian elimination with back-substitution or Gauss-Jordan elimination:
w+x+y+z=5
w+2x-y-2z=-1
w-3x-3y-z=-1
2w-x+2y-z=-2
Answer by nabla(475)   (Show Source):
You can put this solution on YOUR website!1 1 1 1 5
1 2 -1 -2 -1
1 -3 -3 -1 -1
2 -1 2 -1 -2
-R1+R2, -R1+R3
1 1 1 1 5
0 1 -2 -3 -6
0 -4 -4 -2 -6
2 -1 2 -1 -2
-2R1+R4
1 1 1 1 5
0 1 -2 -3 -6
0 -4 -4 -2 -6
0 -3 0 -3 -12
-1/3R4, -1/2R3
1 1 1 1 5
0 1 -2 -3 -6
0 2 2 1 3
0 1 0 1 4
-R2+R1, -R2+R4
1 0 3 4 11
0 1 -2 -3 -6
0 2 2 1 3
0 0 2 4 10
-2R2+R3
1 0 3 4 11
0 1 -2 -3 -6
0 0 6 7 15
0 0 2 4 10
1/2R4 <-> R3
1 0 3 4 11
0 1 -2 -3 -6
0 0 1 2 5
0 0 6 7 15
-3R3+R1,2R3+R2, -6R3+R4
1 0 0 -2 -4
0 1 0 1 4
0 0 1 2 5
0 0 0 -5 -3
-1/5R5
1 0 0 -2 -4
0 1 0 1 4
0 0 1 2 5
0 0 0 1 3/5
-2R4+R3,-R4+R2, 2R4+R1
1 0 0 0 -14/5
0 1 0 0 17/5
0 0 1 0 19/5
0 0 0 1 3/5
This gives solution set {-14/5, 17/5, 19/5, 3/5}.
|
|
|
| |
