Question

If $A={\left[a_{ij}\right]}_{m\times n}$ is a matrix of rank r, then

• A. $r=min(m,n)$
• B. $r<min(m,n)$
• C. $r\le min(m,n)$
• D. none of these

Answer 1

Answer: (C)

$r\le min(m,n)$

Given, $A={\left[a_{ij}\right]}_{m\times n}$
Then, by definition of rank of matrix,
Rank of A is $r\le min(m,n)$