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rock.freak667

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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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