Question 1160071
{{{(matrix(3,5,
1, -2, 3, 1, 2,
1,  1, 4,-1, 3,
2,  5, 9,-2, 8))}}}

-1R1+1R2->R2:

{{{matrix(3,1,-1,1,"")}}}{{{(matrix(3,5,
1, -2, 3, 1, 2,
1,  1, 4,-1, 3,
2,  5, 9,-2, 8))}}}{{{matrix(3,1,"",""="","")}}}{{{(matrix(3,5,
1, -2, 3, 1, 2,
0,  3, 1,-2, 1,
2,  5, 9,-2, 8))}}}

-2R1+1R2->R3:

{{{matrix(3,1,-2,"",1)}}}{{{(matrix(3,5,
1, -2, 3, 1, 2,
0,  3, 1,-2, 1,
2,  5, 9,-2, 8))}}}{{{matrix(3,1,"",""="","")}}}{{{(matrix(3,5,
1, -2, 3, 1, 2,
0,  3, 1,-2, 1,
0,  9, 3,-4, 4))}}}

-3R2+1R3->R3:

{{{matrix(3,1,"",-3,1)}}}{{{(matrix(3,5,
1, -2, 3, 1, 2,
0,  3, 1,-2, 1,
0,  9, 3,-4, 4))}}}{{{matrix(3,1,"",""="","")}}}{{{(matrix(3,5,
1, -2, 3, 1, 2,
0,  3, 1,-2, 1,
0,  0, 0, 2, 1))}}}

2R2+3R1->R1:

{{{matrix(3,1,3,2,"")}}}{{{(matrix(3,5,
1, -2, 3, 1, 2,
0,  3, 1,-2, 1,
0,  0, 0, 2, 1))}}}{{{matrix(3,1,"",""="","")}}}{{{(matrix(3,5,
3,  0,11,-1, 8,
0,  3, 1,-2, 1,
0,  0, 0, 2, 1))}}}

1R3+1R2->R2

{{{matrix(3,1,"",1,1)}}}{{{(matrix(3,5,
3,  0,11, -1, 8,
0,  3, 1,-2, 1,
0,  0, 0, 2, 1))}}}{{{matrix(3,1,"",""="","")}}}{{{(matrix(3,5,
3,  0,11, -1, 8,
0,  3, 1, 0, 2,
0,  0, 0, 2, 1))}}}

1R3+2R1->R1

{{{matrix(3,1,2,"",1)}}}{{{(matrix(3,5,
3,  0,11, -1, 8,
0,  3, 1,  0, 2,
0,  0, 0, 2, 1))}}}{{{matrix(3,1,"",""="","")}}}{{{(matrix(3,5,
6,  0,22,  0,17,
0,  3, 1, 0, 2,
0,  0, 0, 2, 1))}}}

(1/6)R1->R1
(1/3)R2->R2
(1/2)R2->R3

{{{matrix(3,1,"1/6","1/3","1/2")}}}{{{(matrix(3,5,
6,  0,22,  0,17,
0,  3, 1,0, 2,
0,  0, 0, 2, 1))}}}{{{matrix(3,1,"",""="","")}}}{{{(matrix(3,5,
1,  0,"11/3",  0,"17/3",
0,  1, "1/3", 0, "2/3",
0,  0, 0, 1, "1/2"))}}}    <-- answer

Edwin</pre>