Question

Find the rank of $\left[\begin{array}{ccc}3& -1& 2\\ -3& 1& 2\\ -6& 2& 4\end{array}\right]$

Answer 1

$Givenmatrixis\left[\begin{array}{ccc}3& -1& 2\\ -3& 1& 2\\ -6& 2& 4\end{array}\right]$

$Therankofamatrixissaidtoberif$

$1.EveryminorofAoforderr+1iszero$

$2.ThereisatleastoneminorofAoforderrwhichdoesnotvanish$

$\left|\begin{array}{ccc}3& -1& 2\\ -3& 1& 2\\ -6& 2& 4\end{array}\right|=0$

$\left|\begin{array}{cc}3& -1\\ -3& 1\end{array}\right|=0;\left|\begin{array}{cc}-1& 2\\ 1& 2\end{array}\right|\ne 0$

$Hencerankr\left(A\right)=2$