Rank of a Matrix: Determine Value of k

[lalligagger]

Homework Statement

Determine the values of k, if any, that give the matrix (1,1,k),(1,k,1),(k,1,1) a rank of: zero, one, two, or three.

Homework Equations

The Attempt at a Solution

I tried reducing to row echelon form but it's confusing dealing with all the k's. Is there a better approach to this?

 

[yyat]

The row echelon form of this matrix is not very complicated, however it depends on the value of k. So whenever you divide by some value involving k while computing it, you will need to consider special cases (k=1, k=-2).