Question

The rank of the matrix M = $\left[\begin{array}{ccc}5& 10& 10\\ 1& 0& 2\\ 3& 6& 6\end{array}\right]$ is

• A. 0
• B. 1
• C. 2
• D. 3

Answer 1

The correct option is C 2

M = $\left[\begin{array}{ccc}5& 10& 10\\ 1& 0& 2\\ 3& 6& 6\end{array}\right]$

det {M} = 5(0-12)-1 (60-60) +3 (20-0)

= -60 - 0 + 60 =0

The one of the minor of matrix M has non zero determinant value. e.g.

$M_{11}=\left[\begin{array}{cc}0& 2\\ 6& 6\end{array}\right]and\left|M_{11}\right|=-12$

Hence rank of M is 2