What does the rank of a matrix tell you?

[Muthumanimaran]

What does a rank of a matrix mean? why it is important? what does it tells you about?

 

[jedishrfu]

Its described here:

http://www.cliffsnotes.com/math/algebra/linear-algebra/real-euclidean-vector-spaces/the-rank-of-a-matrix

and here:

http://en.wikipedia.org/wiki/Matrix_rank

Basically it will tell you the number of degenerate solutions. They provide some examples too.

Lastly, a video discussion of the matrix and its rank among other things: