A question laws of the inverse

[transgalactic]

in this question my book makes a certain presumption

that some how the ability for the matrix to be inversible
connects to its dim Im

can you say how it works in this question?

http://img441.imageshack.us/my.php?image=img86041mw3.jpg

 

[CompuChip]

Have you learned about linear maps yet? There are some nice relations such as these which will help you out here.

 

[transgalactic]

it doesn't help me much in solving this question
can you please be more spesifiv about where to read in this page
because there are a lot of theory
which i already know

can you answer to my original question

 

[transgalactic]

anyone??

 

[CompuChip]

I linked to a very specific section of that page, namely the one stating

If $f : V \to W$ is linear, we define the kernel and the image or range of f by
:$$\operatorname{ker}(f)=\{\,x\in V:f(x)=0\,\}$$
:$$\operatorname{im}(f)=\{\,w\in W:w=f(x),x\in V\,\}$$
ker(f) is a subspace of V and im(f) is a subspace of W. The following dimension formula, known as the rank-nullity theorem, is often useful:
$$\dim(\ker( f )) + \dim(\operatorname{im}( f )) = \dim( V )$$

Now if you have some knowledge of linear maps and such (which I presume you do, or should have at least, because the book uses terms like kernel and image in the first place), the statement will immediately follow.