Question 1140461
{{{x[1] - 3x[2] - 2x[3] + x4	= -2}}}
{{{-2x[1] + 7x[2] + x[3] - 2x[4]	= -3}}}
{{{3x[1] - 7x[2] - 3x[3] + 3x[4]	= -2}}}
{{{5x[1 ]+ x[2 ]+ 4x[3] -2x[4]	= 16}}}



your matrix:

{{{matrix(4,5,
1,-3,-2,1,-2,
-2,7,1,-2,-3,
3,-7,-3,3,-2,
5,1,4,-2,16)}}}


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

{{{matrix(4,5,
1,	-3,	-2,	1,	-2,
-2,	7,	1,	-2,	-3,
3,	-7,	-3,	3,	-2,
5,	1,	4,	-2,	16)}}}


Eliminate the 1st column:


{{{matrix(4,5,

1,	-3,	-2,	1,	-2,
0,	1,	-3,	0,	-7,
0,	2,	3,	0,	4,
0,	16,	14,	-7,	26)}}}


Find the pivot in the 2nd column in the 2nd row:

{{{matrix(4,5,

1,	-3,	-2,	1,	-2,
0,	1,	-3,	0,	-7,
0,	2,	3,	0,	4,
0,	16,	14,	-7,	26)}}}


Eliminate the 2nd column:


{{{matrix(4,5,

1,	0,	-11,	1,	-23,
0,	1,	-3,	0,	-7,
0,	0,	9,	0,	18,
0,	0,	62,	-7,	138)}}}


Make the pivot in the 3rd column by dividing the 3rd row by {{{9}}}:


{{{matrix(4,5,

1,	0,	-11,	1,	-23,
0,	1,	-3,	0,	-7,
0,	0,	1,	0,	2,
0,	0,	62,	-7,	138)}}}



Eliminate the 3rd column


{{{matrix(4,5,

1,	0,	0,	1,	-1,
0,	1,	0,	0,	-1,
0,	0,	1,	0,	2,
0,	0,	0,	-7,	14)}}}



Make the pivot in the 4th column by dividing the 4th row by {{{-7}}}:


{{{matrix(4,5,

1,	0,	0,	1,	-1,
0,	1,	0,	0,	-1,
0,	0,	1,	0,	2,
0,	0,	0,	1,	-2)}}}



Eliminate the 4th column:


{{{matrix(4,5,

1,	0,	0,	0,	1,
0,	1,	0,	0,	-1,
0,	0,	1,	0,	2,
0,	0,	0,	1,	-2)}}}



Solution set:

{{{x[1] = 1}}}
{{{x[2 ]= -1}}}
{{{x[3] = 2}}}
{{{x[4] = -2}}}