Compute the four fundamental vector spaces associated with A and verify the theorem "If A is a given matrix, then the null space is the orthogonal complement of the row space of A and the null space of is the orthogonal complement of the column space of A."

A=

So far, I got rref(A)=B=

I'm not sure if I am doing this write. The following is my work. Any advice or comments would be greatly appreciated. Thank you!

T={(1, 0, -2, -3), (0, 1, 1, 2)}

and the transpose of A=

rref(transpose of A)=

T'=