Question 152209
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}.