Thread: nontrivial solution for a homogeneous system

Let Show that the homogeneous sytem Ax=0 has only the trivial solution iff ad-bc≠0

I know it has to do with there not being a column of 0s in A.

If the matrix A invertible and the the system Ax=b is consistent for every choice of the column vector b and the unique solution is given by . In the case of a homogeneous system Ax=0, the vector b is 0 and the system has only the trivial solution .