kx + y - z = 0
x + ky - z = 0
2x - y + z = 0
Can't understand the difference between finding k in the systems with trivial and nontrivial solutions. I've solved the same lin.equation, but in the conditions was written " If th following system of homogeneous linier equation has nontrivial zeros, what value k is equal to?" and k was = 4, -1. But in this question answer is -2 and 1
Hint: The system has only the trivial solution iff the coefficient matrix is non-singular. This is so iff the determinant of this matrix is not $0$. The correct answer is $k \neq 1, k \neq -2$.