SOLUTION: Solve the system using an augmented matrix. can you please shoe me the steps for doing this. thank you. 5x + 4y - z = 1 2x - 2y + z = 1 2x - y + z = 2

Algebra ->  Algebra  -> Matrices-and-determiminant -> SOLUTION: Solve the system using an augmented matrix. can you please shoe me the steps for doing this. thank you. 5x + 4y - z = 1 2x - 2y + z = 1 2x - y + z = 2      Log On

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Question 176637: Solve the system using an augmented matrix. can you please shoe me the steps for doing this. thank you.
5x + 4y - z = 1
2x - 2y + z = 1
2x - y + z = 2
Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!
First, pull out the coefficients and the right hand constants to form the augmented matrix:


%28matrix%283%2C4%2C5%2C4%2C-1%2C1%2C2%2C-2%2C1%2C1%2C2%2C-1%2C1%2C2%29%29


Multiply Row 1 by 1%2F5 to make the pivot 1:

%28matrix%283%2C4%2C1%2C4%2F5%2C-1%2F5%2C1%2F5%2C2%2C-2%2C1%2C1%2C2%2C-1%2C1%2C2%29%29

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

%28matrix%283%2C4%2C1%2C4%2F5%2C-1%2F5%2C1%2F5%2C0%2C-18%2F5%2C7%2F5%2C3%2F5%2C2%2C-1%2C1%2C2%29%29

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

%28matrix%283%2C4%2C1%2C4%2F5%2C-1%2F5%2C1%2F5%2C0%2C-18%2F5%2C7%2F5%2C3%2F5%2C0%2C-13%2F5%2C7%2F5%2C8%2F5%29%29

Multiply Row 2 by -5%2F18 to make the pivot 1:

%28matrix%283%2C4%2C1%2C4%2F5%2C-1%2F5%2C1%2F5%2C0%2C1%2C-7%2F18%2C-1%2F6%2C0%2C-13%2F5%2C7%2F5%2C8%2F5%29%29

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

%28matrix%283%2C4%2C1%2C4%2F5%2C-1%2F5%2C1%2F5%2C0%2C1%2C-7%2F18%2C-1%2F6%2C0%2C0%2C7%2F18%2C7%2F6%29%29

Multiply Row 3 by 18%2F7 to make the pivot 1:

%28matrix%283%2C4%2C1%2C4%2F5%2C-1%2F5%2C1%2F5%2C0%2C1%2C-7%2F18%2C-1%2F6%2C0%2C0%2C1%2C3%29%29

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

%28matrix%283%2C4%2C1%2C4%2F5%2C-1%2F5%2C1%2F5%2C0%2C1%2C0%2C1%2C0%2C0%2C1%2C3%29%29


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

%28matrix%283%2C4%2C1%2C4%2F5%2C0%2C4%2F5%2C0%2C1%2C0%2C1%2C0%2C0%2C1%2C3%29%29


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

%28matrix%283%2C4%2C1%2C0%2C0%2C0%2C0%2C1%2C0%2C1%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


Since the right hand column is %28matrix%283%2C1%2C0%2C1%2C3%29%29, this means that x=0, y=1 and z=3