Why do we take the determinant value and why is it equal to zero?

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Write the equations in matrix form and use the theorem - "A square matrix M from the equation Mx = 0 is invertible if and only if this homoegenous system of equations has no non-trivial solution".

In this case, we want a non-trivial solution (as indicated by "x, y and z are not all zero"), so we set the determinant to zero.

In this case, we want a non-trivial solution (as indicated by "x, y and z are not all zero"), so we set the determinant to zero.

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