Question

$A$ is a $m \times n$ matrix of rank 4 . If $A$ contains an $m^{\text {th }}$ order non singular sub matrix and $A^{T} A$ is a $7 \times 7$ matrix, then the number of rows of $A$ is

• A. 5
• B. 6
• C. 7
• D. 4

Answer 1

Answer: (D)

Given, $A$ is $m \times n$ matrix of rank $4$
$A$ contains $m^\text{th}$ order of non-singular sub matrix.
$A$ is non-singular matrix
$\therefore A$ is a square matrix of order $M$
$\therefore $ Rank of $A$ is $M$
$\therefore $ order of $A=4[$ rank of $A=4]$
Hence, rows of $A=4$.