SOLUTION: 1.) {x-y+z=1 {x+y+3z=-3 {2x-y+2z=0

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Question 176992This question is from textbook Prentice Hall Mathematics Algebra 2
: 1.)
{x-y+z=1
{x+y+3z=-3
{2x-y+2z=0 This question is from textbook Prentice Hall Mathematics Algebra 2

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First, extract the coefficients to form the following matrix:


%28matrix%283%2C4%2C1%2C-1%2C1%2C1%2C1%2C1%2C3%2C-3%2C2%2C-1%2C2%2C0%29%29


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

%28matrix%283%2C4%2C1%2C-1%2C1%2C1%2C0%2C2%2C2%2C-4%2C2%2C-1%2C2%2C0%29%29

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

%28matrix%283%2C4%2C1%2C-1%2C1%2C1%2C0%2C2%2C2%2C-4%2C0%2C1%2C0%2C-2%29%29

Multiply Row 2 by 1%2F2 to make the pivot 1:

%28matrix%283%2C4%2C1%2C-1%2C1%2C1%2C0%2C1%2C1%2C-2%2C0%2C1%2C0%2C-2%29%29

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

%28matrix%283%2C4%2C1%2C-1%2C1%2C1%2C0%2C1%2C1%2C-2%2C0%2C0%2C-1%2C0%29%29

Multiply Row 3 by -1 to make the pivot 1:

%28matrix%283%2C4%2C1%2C-1%2C1%2C1%2C0%2C1%2C1%2C-2%2C0%2C0%2C1%2C0%29%29


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

%28matrix%283%2C4%2C1%2C-1%2C1%2C1%2C0%2C1%2C0%2C-2%2C0%2C0%2C1%2C0%29%29


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

%28matrix%283%2C4%2C1%2C-1%2C0%2C1%2C0%2C1%2C0%2C-2%2C0%2C0%2C1%2C0%29%29


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

%28matrix%283%2C4%2C1%2C0%2C0%2C-1%2C0%2C1%2C0%2C-2%2C0%2C0%2C1%2C0%29%29


The matrix is now in reduced row echelon form

If you need more help with row reduction, check out the Linear Algebra Toolkit


Since the right hand column is %28matrix%283%2C1%2C-1%2C-2%2C0%29%29 this means that the solutions are x=-1, y=-2 and z=0