1. The problem statement, all variables and given/known data 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 2. Relevant equations Tried sticking it into a matrix: [1 1 k | 1] [1 k 1 | 1] [k 1 1 | 1] 3. 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 :).