Question 1137455
{{{x + y+ 4z = 6}}}
{{{3x+ 2y -2z =9}}}
{{{5x + y+ 2z =13 }}}


Your matrix

{{{matrix(3,4, 1,	1,	4,	6,
	3,	2,	-2,	9,
	5,	1,	2,	13)}}}



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

{{{matrix(3,4,1,	1,	4,	6,
3,	2,	-2,	9,
5,	1,	2,	13)}}}



Eliminate the 1st column

{{{matrix(3,4,
1,	1,	4,	6,
0,	-1,	-14,	-9,
0,	-4,	-18,	-17)}}}



Find the pivot in the 2nd column in the 2nd row (inversing the sign in the whole row)


{{{matrix(3,4,
1,	1,	4,	6,
0,	1,	14,	9,
0,	-4,	-18,	-17)}}}



Eliminate the 2nd column


{{{matrix(3,4,
1,	0,	-10,	-3,
0,	1,	14,	9,
0,	0,	38,	19)}}}


Make the pivot in the 3rd column by dividing the 3rd row by {{{38}}}

{{{matrix(3,4, 
1,	0,	-10,	-3,
0,	1,	14,	9,
0,	0,	1,	1/2)}}}



Eliminate the 3rd column

{{{matrix(3,4, 
1,	0,	0,	2,
0,	1,	0,	2,
0,	0,	1,	1/2)}}}


Solution set:

{{{x = 2}}}
{{{y = 2}}}
{{{z = 1/2}}}