finding ranks and linearly independent columns and rows.

[cool.man]

Hi,
I want to know that how to find the rank of a matrix and how to figure out that the columns or rows are linearly independent.what is the defination for linear independent
suppose i have a matrix A

| 0 1 1 2 |
| 1 2 3 4 |
| 2 0 2 0 |

then how to find rank and linearly independent columns.
In the book it is given that the rank of the given matrix is 2 and two linear independent columns are there.

 

[htg]

You can notice that column 4 is just column 2 multiplied by 2, and that the 3rd column is the sum of the first two columns. This leaves you with the first two columns. None of them is a multiple of the other, so you have 2 linearly independent columns.