Question

The rank of the matrix, M = $\left[\begin{array}{ccc}0& 1& 1\\ 1& 0& 1\\ 1& 1& 0\end{array}\right]$ is

Answer 1

Given data

M = ${\left[\begin{array}{ccc}0& 1& 1\\ 1& 0& 1\\ 1& 1& 0\end{array}\right]}_{3\times 3}$

Determinant of M

$\left|M\right|=\left|\begin{array}{ccc}0& 1& 1\\ 1& 0& 1\\ 1& 1& 0\end{array}\right|$

= 0(0 - 1) - 1(0 - 1) +1(1 - 0)

= 1 + 1 = 2

$\because \left|M\right|\ne 0$

Hence, rank of the matrix is '3'