Rank of a Matrix

The above matrix has a zero determinant and is therefore singular. It has no inverse. It has two identical rows. In other words, the rows are not independent. If one row is a multiple of another, then they are not independent, and the determinant is zero. (Equivalently: If one column is a multiple of another, then they are not independent, and the determinant is zero.)

The rank of a matrix is the maximum number of independent rows (or, the maximum number of independent columns). A square matrix A_n×n is non-singular only if its rank is equal to n.

QUESTION 15:

What is the rank of the following matrix?


 1   2   0   3
 1  -2   3   0
 0   0   4   8
 2   4   0   6