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Question 34228: Render the augmented matrix:
1 0 -1|2
0 2 1 |-1
1 0 1 |0
into row-echelon form and determine the value of the variables x,y and z.
Also:
2.)
Find the values of this matrix:
1 0 -1|0
0 1 0 |1
0 0 1 |2
Answer by kietra(57)   (Show Source):
You can put this solution on YOUR website! First of all, row echelon form means that there are all 1's across the diagonal and everthing except the diagonal and the column on the far right are zeros. You can manipulate the matrix anyway you would like and there are many different ways to do so. Here is one way.
1 0 -1 | 2
0 2 1 |-1
1 0 1 | 0
First, subtract line 3 from line 1 and use that to replace line 3:
1 0 -1 | 2
0 2 1 |-1
0 0 -2 | 2
Next, divide line 3 by -2 and replace that in line 3:
1 0 -1 | 2
0 2 1 |-1
0 0 1 |-1
Then add line 3 to line 1 and replace line 1:
1 0 0 | 1
0 2 1 |-1
0 0 1 |-1
Then subtract line 3 from line 2 and replace that in line 2:
1 0 0 | 1
0 2 0 | 0
0 0 1 |-1
Last, divide line 2 by 2
1 0 0 | 1
0 1 0 | 0
0 0 1 |-1
So
x = 1
y = 0
z = -1
Make sure to check your solutions!
(#2)
1 0 -1|0
0 1 0 |1
0 0 1 |2
First, add row 3 to row 1 and replace row 1:
1 0 0 |2
0 1 0 |1
0 0 1 |2
x=2
y=1
z=2
Check your solutions. :)
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