Question 1129786

Your matrix:


{{{matrix(3,4,
1,	1,	1,	0,
2,	-1,	3,	0,
1,	0,	-1,	6)}}}


Find the pivot in the 1st column in the 1st row:


{{{matrix(3,4,
1,	1,	1,	0,
2,	-1,	3,	0,
1,	0,	-1,	6)}}}



Eliminate the 1st column:

{{{matrix(3,4,

1,	1,	1,	0,
0,	-3,	1,	0,
0,	-1,	-2,	6)}}}


Find the pivot in the 2nd column (inversing the sign in the whole row) and swap the 3rd and the 2nd rows

{{{matrix(3,4,

1,	1,	1,	0,
0,	1,	2,	-6,
0,	-3,	1,	0)}}}



Eliminate the 2nd column


{{{matrix(3,4,

1,	0,	-1,	6,
0,	1,	2,	-6,
0,	0,	7,	-18)}}}



Make the pivot in the 3rd column by dividing the 3rd row by 7



{{{matrix(3,4,

1,	0,	-1,	6,
0,	1,	2,	-6,
0,	0,	1,	-18/7)}}}



Eliminate the 3rd column

{{{matrix(3,4,


1,	0,	0,	24/7,
0,	1,	0,	-6/7,
0,	0,	1,	-18/7)}}}

Solution set:

{{{x[1] = 24/7}}}

{{{x[2] = -6/7}}}

{{{x[3] = -18/7}}}