The maximum number of linearly independent eigenvectors of the matrix
\(\left(\begin{array}{llll} 1 & 1 & 0 & 0 \\ 2 & 2 & 0 & 0 \\ 0 & 0 & 3 & 0 \\ 0 & 0 & 1 & 3 \end{array}\right)\)
is equal to ____________.
Enter numerical value using the virtual keypad. Round off where necessary.