- #1

rafehi

- 49

- 1

## Homework Statement

Determine the values of k for which the system of linear equations has (i) no solution vector, (ii) a unique solution vector, (iii) more than one solution vector (x,y,z):

kx + y + z = 1

x + ky + z = 1

x + y + kz = 1

**2. The attempt at a solution**

The only approach I can think of is reducing it to row echelon form, but given the k's I'm finding it impossible to do so. Putting it in augmented matrix form and reducing it as best I can, I get:

[k 1 1 | 1]

[0 (k-1) (1-k) | 0]

[1 1 k | 1]

The above is getting me nowhere. I've tried taking out factors of k, but I'm not sure if that's the way to go because the end result is overly complicated.

Any help?