- #1
Fluorescent
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- 0
Homework Statement
Determine the values of k for which the system of linear equations has (i) a unique solution, (ii) no solution, (iii) infinitely many solutions. Write down the complete solution in cases (i) and (iii):
x + y + kz = 1
x + ky + z = 1
kx + y + z = 1
Homework Equations
Tried sticking it into a matrix:
[1 1 k | 1]
[1 k 1 | 1]
[k 1 1 | 1]
The Attempt at a Solution
I'm aware I then need to get that matrix into some sort of Reduced Echelon Form so I can analyse things from it. This is what I'm finding difficult as the best I can ever get is:
[(k+2) (k+2) (k+2) | 3]
[ 0 (k-1) (k-1) | 0]
[ 1 1 k |1]
That's not even close to be honest.
I can already see that k=1 is when there's an infinite solution (as is pretty obvious) but even that I can't actually prove.
Any guidance would be a appreciated, thank you :).