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Homework Statement
Find the condition of k such that the set of equations x+y-z=1, x+2y+kz=-1, x+ky-z=1,
has a unique soltuion,infinite sol'n or no solution.
Homework Equations
The Attempt at a Solution
In the augemented matrix form
[1 1 -1 1]
[1 2 k -1]
[1 k -1 -1]
R2-R1,R3-R1
[1 1 -1 1]
[0 1 (k+1) -2]
[0 (k-2) -(k+1) -2]
R3-(k-2)R2
[1 1 -1 1]
[0 1 (k+1) -2]
[0 0 -(k+1)(k+3) (2k-6)]
For a unique solution.
[itex]-(k+1)(k+3) \neq 0[/itex] so that [itex]k \neq 1,3[/itex]
For infinite soltutions -(k+1)(k+3)=0 AND 2k-6=0
so that k=-1,-3 AND k=3
This doesn't make sense to me, as k can only be on value at a time, and if k=3, there will be no solution as the ranks of the augmented matrix and the initial matrix won't be the same.
SO where in my row reduction did I go wrong?
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