Shortcut To Find Rank Of Matrix :
- Look at the matrix whether it is rectangular or square matrix.
- For rectangular matrix, if number of rows is less than number of columns then the rank of matrix will be equal to number of linearly independent rows.Similarly, If number of columns is less than number of rows then rank of matrix will be equal to number of linearly independent columns.
- For square matrix, number of linearly independent rows or columns is called rank of matrix.
Now, You can see, column 1 and 2 are independent because they are not derived form others. but column 3 (C1 + C2) is sum of column 1 and column 2. So there are two linearly independent columns hence its rank is 2.
Now, most of us don't know what is meant by linearly independent rows or columns.
Linearly Independent Rows/Columns : The rows/columns which is not derived from other rows/columns (scalar multiple of other rows/columns or sum of two rows/columns) i.e. which don't depend on other rows/columns.
For example :
