Hi guys I am trying to figure out the following question can anyone help:

Find $\displaystyle \lambda$ for the Linear System:

$\displaystyle \lambda$x+y+z=1

x+$\displaystyle \lambda$y+z=1

x+y+$\displaystyle \lambda$z=1

For infinite solutions.

A unique solution.

And it's not asked but no solutions I wouldn't mind knowing either.

I understand how to do these with numbers