Dimension - Linear Algebra

There are these questions in the book that ask us to find the Dimension of a particular space. Do I just find a basis for the space, and then the number of elements in that basis is the dimension for the space? Or is there some trick to finding the dimension? Thanks!

-----------
For example, the first one the book asks is: Find the dimension of 2x2 matricies. So a basis for 2x2 matricies is the following set:

$$\left\{\left(\begin{array}{cc}1&0\\0&0\end{array}\right), \left(\begin{array}{cc}0&1\\0&0\end{array}\right), \left(\begin{array}{cc}0&0\\1&0\end{array}\right), \left(\begin{array}{cc}0&0\\0&1\end{array}\right)\right\}$$

And this basis has 4 elements, so the dimension of 2x2 matricies is 4.
---------

Is that basically how these problems go? Thanks.
 PhysOrg.com science news on PhysOrg.com >> New language discovery reveals linguistic insights>> US official: Solar plane to help ground energy use (Update)>> Four microphones, computer algorithm enough to produce 3-D model of simple, convex room

Recognitions:
Gold Member
Homework Help