Have youtriedanything yourself? In particular, have you tried to solve for x, y, and z to seeifyou get a "zero solution" (x= y= z= 0) and what might prevent you?

From the first equation, x- ky- z= 0, z= ky- x. Putting that into the third equation, x+ y+ z= 0, x+ y+ ky- x= y+ ky= (1+ k)y= 0. Now, if the product of two numbers is 0, then at least one of them must be 0. So either y= 0 or ....