If its homogeneous system has a nontrivial solution, then the determinant of the coefficient matrix must be zero. We need to find how many distinct $α \in [0, π]$ are possible.

The determinant is given by:
$111 sin α cos α sin 2 α sin^{2} α cos^{2} α sin^{2} 2 α = 0$

Question

If its homogeneous system has a nontrivial solution, then the determinant of the coefficient matrix must be zero. We need to find how many distinct $α \in [0, π]$ are possible.

The determinant is given by:

$111 sin α cos α sin 2 α sin^{2} α cos^{2} α sin^{2} 2 α = 0$

TestHub · Accepted Answer

The determinant factors as ( sin α − cos α ) ( cos α − sin 2 α ) ( sin 2 α − sin α ) . Solving on [ 0 , π ] gives seven distinct values.

Mathematics - Determinant Question with Solution | TestHub

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