SOLUTION: find k if kx+y+z=4-k x+ky+z=2+k x+y+kz=3 for 1-unique solu 2-infinite solu 3-no solu

Question 1015937: find k if
kx+y+z=4-k
x+ky+z=2+k
x+y+kz=3
for
1-unique solu
2-infinite solu
3-no solu
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
Look at the coefficient matrix,

Find the determinant,

So and are solutions.
When ,

and the right hand side becomes,

So this system is dependent and has infinitely many solutions.
.
.
When ,

and the right hand side becomes,
.
In this case, it is an inconsistent system because ,
, and ,
.
.
For all other values of k, you would have a unique solution.
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