The rank of $\left[\begin{array}{ccc}1 & -1 & 1 \ 1 & 1 & -1 \ -1 & 1 & 1\end{array} ight]$ is

Question

The rank of $\left[\begin{array}{ccc}1 & -1 & 1 \ 1 & 1 & -1 \ -1 & 1 & 1\end{array}ight]$ is

Aicharya · Accepted Answer

$ \begin{aligned} & 	ext { Let } A=\left[\begin{array}{ccc} 1 & -1 & 1 \ 1 & 1 & -1 \ -1 & 1 & 1 \end{array}ight] \ & 	herefore \quad|A|=1(1+1)+1(1-1)+1(1+1) \ & =4 
eq 0 \ & \end{aligned} $ $	herefore$ Rank of matrix $A$ is 3

The rank of $\left[\begin{array}{ccc}1 & -1 & 1 \\ 1 & 1 & -1 \\ -1 & 1 & 1\end{array}\right]$ is

Solution