For what value of t does the homogeneous system of equations

have non-zero solutions?

　　 Solution: According to Clem's rule, if the given system of homogeneous linear equations has a non-zero solution, then its coefficient determinant . Using the properties of determinants and the determinant expansion theorem, we can calculate

　　So, if a system of homogeneous linear equations has non-zero solutions, then

,

That is, when or or , the system of homogeneous linear equations has non-zero solutions.