First time poster. Have attempted the problem, but keep hitting dead ends and have no idea how to proceed.(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

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?

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# Linear Algebra (finding values of a constant k to give no/unique/infinite solutions)

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