Non-trivial solution

For what values of p, these equations have non-trivial solution.

How to solve this question. And also tell me what is meant by non-trivial solution

These can all be written in the form



which obviously has the solution x= y= z= 0. That is the "trivial" solution. If the coefficient matrix
has determinant 0 (is not invertible) then there will also exist other "non-trivial" solutions.