Question 934468
3x-4y-z=-1
x=y-z=-2.....I believe after x comes + sign
2x-5y=2z=13...after 5y comes + sign

{{{3x-4y-z=-1}}}
{{{x+y-z=-2}}}
{{{2x-5y+2z=13 }}}



Initial Matrix 
{{{3}}} 	{{{-4}}} 	{{{-1}}} 	{{{-1}}}
{{{1}}} 	{{{1}}} 	{{{-1}}} 	{{{-2}}}
{{{2}}} 	{{{-5}}} 	{{{2}}} 	{{{13}}}


Taking matrix to echelon form:


multiplying row {{{1}}} by 0.3333}}}
adding {{{-1}}} times row {{{1}}} to row {{{2}}}
adding {{{-1}}} times row {{{1}}} to row {{{3}}}
multiplying row {{{2}}} by {{{0.4286}}}
adding {{{2.3333}}} times row {{{2}}} to row {{{3}}}
multiplying row {{{3}}} by {{{0.5}}}


{{{1}}} 	{{{-1.3333}}} 	{{{-0.3333}}} 	{{{-0.3333}}}
{{{0}}} 	{{{1}}} 	{{{-0.2857}}} 	{{{-0.7143}}}
{{{0}}} 	{{{0}}} 	{{{1}}} 	{{{6}}}


Taking matrix to reduced echelon form:

adding 1.3333 times row 2 to row 1
adding 0.7143 times row 3 to row 1
adding 0.2857 times row 3 to row 2

Reduced echelon form:

{{{1}}} 	{{{0}}} 	{{{0}}} 	{{{3}}}
{{{0}}} 	{{{1}}} 	{{{0}}} 	{{{1}}}
{{{0}}} 	{{{0}}} 	{{{1}}} 	{{{6}}}

Result:
{{{x = 3}}}
{{{y= 1}}}
{{{z= 6}}}