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)
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?
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)
0
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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)