Let the matrix $A = [a_{ij}]_{3×3}$ be defined by $a_{ij}=\left\{\begin{matrix}2i+3j,&i<j\\5,&i=j\\3i-2j,&i>j\end{matrix}\right.$. The number of elements in the matrix A which are greater than 7, is:

3

The correct answer is Option (2) → 2

$A = [a_{ij}]_{3\times 3}$

Compute all 9 entries:

$a_{11}=5$

$a_{12}=2\cdot 1 + 3\cdot 2 = 8$

$a_{13}=2\cdot 1 + 3\cdot 3 = 11$

$a_{21}=3\cdot 2 - 2\cdot 1 = 4$

$a_{22}=5$

$a_{23}=2\cdot 2 + 3\cdot 3 = 13$

$a_{31}=3\cdot 3 - 2\cdot 1 = 7$

$a_{32}=3\cdot 3 - 2\cdot 2 = 5$

$a_{33}=5$

Elements $>7$ are: $8, 11, 13$

$3$