My text is not helping at all and the wikipedia explanations of the concepts: nullspace and range are way over my head.
Given A is a 3x3 matrix
0 1 0
0 0 1
0 0 0
and B is also a 3x3 matrix
0 0 0
1 0 0
0 1 0
specify the nullspace of A and B, and the range of A and B
Thanks
Note that elementry row operations will change the column space of a matrix.
the span of the columns is
This is the yz plane.
Note that elementry row operation will NOT change the null space.
solving the augmented matrix
in reduced row form
so parameterizing the solution
so we get...
So the null space is all points on the z-axis.