<PRE><B>Question 316592</B>
Use the Gauss - Jordan method to solve the following system of equations. 
2x + y - z = -1 
x - 2y + 2z = 7 
3x + y + z = 4
-----
write out the coefficients and the constant as follows:
  x    y   z   c
  2    1  -1  -1
  1   -2   2   7
  3    1   1   4 (add row 3 to row 1)
-----------------
  5    2   0   3 (add row 1 to row 2)
  1   -2   2   7
  3    1   1   4 
-----------------
  5    2   0   3
  6    0   2  10
  3    1   1   4 (multiply row 3 by -2)
-----------------
  5    2   0   3
  6    0   2  10 (add row 2 to row 3)
 -6   -2  -2  -8 
----------------
  5    2   0   3
  6    0   2  10
  0   -2   0   2 (add row 3 to row 1)
----------------
  5    0   0   5 (divide row 1 by 5)
  6    0   2  10 (divide row 2 by 2)
  0   -2   0   2 (divide row 3 by -2)
----------------
  1    0   0   1 (multiply row 1 by -3)
  3    0   1   5
  0    1   0  -1   
----------------
 -3    0   0  -3 (add row 1 to row 2)
  3    0   1   5
  0    1   0  -1
----------------
 -3    0   0  -3 (lastly divide row 1 by -3)
  0    0   1   2
  0    1   0  -1
----------------
  1    0   0   1
  0    0   1   2
  0    1   0  -1 (rearrange these 3 rows)
-----------------
  1    0   0   1
  0    1   0  -1
  0    0   1   2
-----------------
we wanted to get to the last matrix shown, it is the identity matrix, it has a nice neat diagonal of 1&#39;s and the answers are all in the last column

x =  1
y = -1
z =  2

check: 
2x + y - z = -1 
x - 2y + 2z = 7 
3x + y + z = 4

2(1) + (-1) - (2)  = 2 - 1 - 2 = 2 - 3 = -1
(1) - 2(-1) + 2(2) = 1 + 2 + 4 = 7
3(1) + (-1) + (2)  = 3 - 1 + 2 = 2 + 2 = 4
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