Question 1149664

given the following system of equations:

{{{4 x+  2 y+  3 z= 4}}}

{{{5 x +  6 y+    z  = 2 }}}

{{{2 x+  3 y= -1}}}


using Gauss-Jordan elimination:


Your matrix

{{{matrix(3,4, 4,	2,	3,	4,
5,	6,	1,	2,
2,	3,	0,	-1)}}}


Make the pivot in the 1st column by dividing the 1st row by {{{4}}}


{{{matrix(3,4,1,	1/2,	3/4,	1,
5,	6,	1,	2,
2,	3,	0,	-1)}}}


Eliminate the 1st column

{{{matrix(3,4,1,	1/2,	3/4,	1,
0,	7/2,	-11/4,	-3,
0,	2,	-3/2,	-3)}}}


Make the pivot in the 2nd column by dividing the 2nd row by {{{7/2}}}


{{{matrix(3,4,1,	1/2,	3/4,	1,
0,	1,	-11/14,	-6/7,
0,	2,	-3/2,	-3)}}}


Eliminate the 2nd column

{{{matrix(3,4,1,	0,	8/7,	10/7,
0,	1,	-11/14,	-6/7,
0,	0,	1/14,	-9/7)}}}


Make the pivot in the 3rd column by dividing the 3rd row by {{{1/14}}}

{{{matrix(3,4,1,	0,	8/7,	10/7,
0,	1,	-11/14,	-6/7,
0,	0,	1,	-18)}}}


Eliminate the 3rd column


{{{matrix(3,4,1,	0,	0,	22,
0,	1,	0,	-15,
0,	0,	1,	-18)}}}




The solutions are:

{{{x=22}}} 
{{{y=-15}}}
{{{ z=-18}}}