Question

Find the rank of the matrix
$\left[\begin{array}{cccc}6& 3& 4& 7\\ 2& 1& 0& 1\end{array}\right]$

• A. $3$
• B. $2$
• C. $4$
• D. $1$

Answer 1

The correct option is B $2$

Given matrix is

$\left(\begin{array}{cccc}6& 3& 4& 7\\ 2& 1& 0& 1\end{array}\right)$

Applying $R_1\to R_1-\frac{1}{3}{R}_2$

$\left(\begin{array}{cccc}6& 3& 4& 7\\ 0& 0-\frac{4}{3}& \frac{-4}{3}& \end{array}\right)$

Therefore Rank of matrix= Number of non zero rows in upper triangular matrix

$\therefore$Rank=$2$