Question 1134302

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


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

Make zeros in column {{{1}}} except the entry at row {{{1}}}, column {{{1}}} (pivot entry).

Subtract row {{{1}}} from row{{{ 2}}}:

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

Subtract row {{{1}}} multiplied by {{{2}}} from row {{{3}}}

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

Make zeros in column {{{2}}} except the entry at row{{{ 2}}}, column {{{2 }}}(pivot entry).

Divide row {{{2}}} by {{{-2}}}:

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


Subtract row {{{2}}} from row {{{1}}}:

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

Add row {{{2}}} to row {{{3}}}:

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

Make zeros in column {{{3}}} except the entry at row{{{ 3}}}, column{{{ 3}}}(pivot entry).

Add row {{{3}}} to row {{{1}}}:


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

Divide row {{{3}}} by {{{-3}}}:


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

Add row {{{3}}} multiplied by {{{2}}} to row {{{2}}}

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

Answer:  the reduced row echelon form is
A[ref]={{{matrix(3,4,
1,0,0,-3,
0,1,0,1,
0,0,1,1)}}}