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solving equation system using Gauss method

How can i solve this equation method using the Gauss method?? I have no clue :S

x  -  y + 2z +   t = 0
       y -    z + 2t = 0
2x      + z         =  0


???
0
axtur
Asked:
axtur
1 Solution
 
SyntheticsCommented:
Hope this isn't homework ;-)


First transform the set of linear equations into a matrix.
Then use the 5 row transformations to put the matrix into echelon form.
Rewrite this new matrix as a set of linear equations.
Identify the pivot variables.
Express the pivot variables in terms of the non-pivot variable (one by one)
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Infinity08Commented:
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ozoCommented:
1*x  + -1*y + 2*z  +  1*t = 0
0*x  +  1*y + -1*z +  2*t = 0
2*x  + 0*y  +  1*z  + 0*t = 0
[x y z t]
*
[1 -1 2 1
0  1 -1 2
2 0 1 0]
=
[
0
0
0
]
3 equations in 4  unknowns is underdetermined, but you can let any one be an arbitrary value
(as long as it does not leave a singular matrix)
and solve for the other three in terms of that one
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axturAuthor Commented:
I'm having trouble with the 4th unknown having only 3 equations. So I have to leave the solution in terms of the value of t?
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ozoCommented:
You could leave it in terms of the value of t, or in terms if the value of y, or in terms of the value of x+y
any of them can determine the value of the others, `
and by choosing different values you can generate an infinite number of points that are solutions to the equations.  (all of which lie on the same line)
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