Question 176637
First, pull out the coefficients and the right hand constants to form the augmented matrix:



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



Multiply Row 1 by {{{1/5}}} to make the pivot 1:


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


 Add  -2*Row 1 to Row 2 to get the new Row 2


{{{(matrix(3,4,1,4/5,-1/5,1/5,0,-18/5,7/5,3/5,2,-1,1,2))}}}


 Add  -2*Row 1 to Row 3 to get the new Row 3


{{{(matrix(3,4,1,4/5,-1/5,1/5,0,-18/5,7/5,3/5,0,-13/5,7/5,8/5))}}}


Multiply Row 2 by {{{-5/18}}} to make the pivot 1:


{{{(matrix(3,4,1,4/5,-1/5,1/5,0,1,-7/18,-1/6,0,-13/5,7/5,8/5))}}}


 Add  13/5*Row 2 to Row 3 to get the new Row 3


{{{(matrix(3,4,1,4/5,-1/5,1/5,0,1,-7/18,-1/6,0,0,7/18,7/6))}}}


Multiply Row 3 by {{{18/7}}} to make the pivot 1:


{{{(matrix(3,4,1,4/5,-1/5,1/5,0,1,-7/18,-1/6,0,0,1,3))}}}


Add 7/18*Row 3 to Row 2 to replace Row 2


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



Add 1/5*Row 3 to Row 1 to replace Row 1


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



Add -4/5*Row 2 to Row 1 to replace Row 1


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



The matrix is now in <font size=4><b>reduced row echelon form</b></font>


If you need more help with row reduction, check out the <a href="http://www.math.odu.edu/~bogacki/lat/">Linear Algebra Toolkit</a>



Since the right hand column is {{{(matrix(3,1,0,1,3))}}}, this means that {{{x=0}}}, {{{y=1}}} and {{{z=3}}}