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

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- November 17th 2010, 02:13 AMkumaran5555Non-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 - November 17th 2010, 02:18 AMHallsofIvy
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.