Question

Condition for non trivial solution of homogeneous equation

Answer 1

For a homogeneous system of equations ax+by=0 and cx+dy=0, the situation is slightly different. ... A nxn homogeneous system of linear equations has a unique solution (the trivial solution) if and only if its determinant is non-zero. If this determinant is zero, then the system has an infinite number of solutions.

Answer 2

Answer:

A nxn nonhomogeneous system of linear equations has a unique non-trivial solution if and only if its determinant is non-zero. If this determinant is zero, then the system has either no nontrivial solutions or an infinite number of solutions.