SOLUTION: -x+y+3z=6 x+y+2z=7 2x+3y+z=4

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Question 107919: -x+y+3z=6
x+y+2z=7
2x+3y+z=4
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Start with the given system
system%28-x%2By%2B3z=6%2Cx%2By%2B2z=7%2C2x%2B3y%2Bz=4%29

Write all of the coefficients and the right side constants in an augmented matrix

%28matrix%283%2C4%2C-1%2C1%2C3%2C6%2C1%2C1%2C2%2C7%2C2%2C3%2C1%2C4%29%29



Multiply Row 1 by -1%2F1 to make the pivot 1:

%28matrix%283%2C4%2C1%2C-1%2C-3%2C-6%2C1%2C1%2C2%2C7%2C2%2C3%2C1%2C4%29%29

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

%28matrix%283%2C4%2C1%2C-1%2C-3%2C-6%2C0%2C2%2C5%2C13%2C2%2C3%2C1%2C4%29%29

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

%28matrix%283%2C4%2C1%2C-1%2C-3%2C-6%2C0%2C2%2C5%2C13%2C0%2C5%2C7%2C16%29%29

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

%28matrix%283%2C4%2C1%2C-1%2C-3%2C-6%2C0%2C1%2C5%2F2%2C13%2F2%2C0%2C5%2C7%2C16%29%29

Add -5*Row 2 to Row 3 to get the new Row 3



Multiply Row 3 by -2%2F11 to make the pivot 1:

%28matrix%283%2C4%2C1%2C-1%2C-3%2C-6%2C0%2C1%2C5%2F2%2C13%2F2%2C0%2C0%2C1%2C3%29%29


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

%28matrix%283%2C4%2C1%2C-1%2C-3%2C-6%2C0%2C1%2C0%2C-1%2C0%2C0%2C1%2C3%29%29



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

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


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

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