posted by chris .
If A is a nonsingular matrix, what is the null space of A?
If A is nonsingular then the equation:
A x = y
has a unique solution. Now, the equation:
A x = 0
always has a solution:
x = 0.
If A is nonsingular, then this must thus be the only solution. This means that the null space of A is the zero dimensional vector space containing only the null vector 0.