Does the Equation Ax=0 Have a Nontrivial Solution?

Fact. The homogeneous equation Ax = 0 has a nontrivial solution if and only if the equation has at least one free variable.

Does the equation Ax 0 have a nontrivial solution How do you know?

The equation Ax  0 does have non-trivial solutions because not every column of A has a pivot position. ... The equation Ax  0 does have non-trivial solutions because not every column of A has a pivot position.

Which equation has non-trivial solution?

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.