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.

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- Jan 26th 2011, 08:53 PMsuperdudenontrivial 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. - Jan 26th 2011, 09:21 PMharish21
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 .