# Question:Why doesn't solve give any indication that there can be a non-trivial solution to this system of two linear equations?

## Question:Why doesn't solve give any indication that there can be a non-trivial solution to this system of two linear equations?

Maple

I created the following worksheet to illustrate my question.

We have two equations.  and  are parameters and we wish to solve for  and .

=

=

=

Maple says the only solution is the trivial solution.

If we check the determinant of the matrix of the system we see it can be zero for certain values of  given .

=

=

 (1)

If  is one of these values then the system of equations is singular and has non-zero solutions.

For example, subbing the first value above into the equations and solving Maple gives us non-trivial solutions.

 (2)

Why didn't Maple give us any indication that there could be non-zero solutions in the first call to ?

For context, the system of equations comes from a calculation involving coupled oscillators.

I had a system of differential equations, guessed at a solution, plugged it in and got the equations shown in the worksheet. The guess isn't a correct solution in general, but it is a solution if w is one of the values computed in the worksheet (the values of the variable "solutions").