Question

Let $A=(a_{ij})_{m\times n}$ be a matrix such that $a_{ij}=1$ for all I, j. Then

• A. rank (A) > 1
• B. rank (A) = 1
• C. rank (A) = m
• D. rank (A) = n

Answer 1

Answer: (B)

rank (A) = 1

Answer 2

Rank A = 1 [$\therefore$ every minor of order 2 = 0 and there exists at least one minor of order 1 which is $\neq$ 0 since $a_{ij}$ = 1 for all i,j]