Question 1131187

First write down the augmented matrix and begin Gauss-Jordan elimination:


Your matrix:

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


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

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


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

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


Eliminate the 2nd column:

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


Make the pivot in the 3rd column by dividing the 3rd row by 2:

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


Eliminate the 3rd column:

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


Solution set:

{{{x = 9/2}}}
{{{y = 0}}}
{{{z = -1/2}}}

check your answer: Answer({{{3-3z}}},{{{ 1+2z}}}, {{{z}}}) 

{{{x=3-3z=3-3(-1/2)=3+3/2=6/2+3/2=9/2}}}

{{{y=1+2z=1+2(-1/2)=1-1=0}}}

({{{3-3z}}},{{{ 1+2z}}}, {{{z}}}) =({{{9/2}}},{{{ 0}}}, {{{-1/2}}}) 



Your matrix:

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


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

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


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

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


Eliminate the 2nd column:

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


Solution set:

The system is inconsistent

The system of equations corresponding to this REF has as its third equation
{{{0*x + 0*y + 0*z =4}}}
This equation clearly has no solutions - no assignment of numerical values to {{{x}}}, {{{y}}} and{{{ z}}} will make the value of the expression {{{0*x + 0*y + 0*z}}} equal to anything but zero. Hence the system has no solutions.