I cant understand the how to get the last step

[Intothephy7]

Hi guys.

Please look at the picture.
http://img152.imageshack.us/img152/5664/ortoganel.jpg

I know "First, a basis for the null space of A consists of the vectors: "
I know how to get the orthoganal vectors for A ( NULL(A))

what do they mean by
Now a basis for the orthogonal complement of the null space of A consists of the vectors:

does anyone know how to get that. steps to get that?

 

[Fredrik]

A takes n-component vectors to m-component vectors. (Do you see what n and m are?) The null space of A is a d-dimensional subspace of the n-dimensional vector space which is the domain of A. (You should know what d is by now, if you have done the first part). The orthogonal complement of null(A) is the (n-d)-dimensional subspace that consists of vectors that are orthogonal to all the vectors in null(A).

If you want more help than that, you need to show us how far you can get with this information. Next time you want to ask about a textbook-style question, post in the homework forum (even if it isn't really homework...it's a forum policy thing). I have requested that this thread be moved there.