- Thread starter
- #1

#### Bruce Wayne

##### Member

- Apr 6, 2013

- 16

OK. I want to prove that the columns of matrix

*A*span R

^{n}and that this is equivalent to the linear transformation x->

*A*x maps R

^{n}onto R

^{n}. I would like to prove the converse is also true.

So my thinking is:

Assume the columns of matrix

*A*span R

^{n}. By the definition of

*A*x , for each

**b**in R

^{n}, the equation

*A*x=

**b**has a solution. This implies that

*T*(x)=

**b**has at least one solution.

That's when I get myself totally confused. I think I'm missing a few intermediary steps in the proof. How do I do this proof?