Column and Null space proof!
The question is :
A be an m×n matrix and B an n×r matrix. If AB = O (the m×r matrix of zeroes)
prove that the column space of B is contained in the null space of A.
Here is what I have gotten:
Where the null space is the span of the set of all vectors x that satisy the equation. Let null space(A) = span( ) I let col. space(B)=span( )
Let v be in the col. space(B)
Therefore where are elements of
If we can show that v can be shown to be apart of the span( ) then we are done. I cant think of a way to go about doing this.
Any help would be greatly appreciated!