Let \(A = [a_{ij}]\) be a square matrix of order 3 whose elements are given by \(a_{ij} = i\) if \(i \ge j\), and \(a_{ij} = j\) if \(i \lt j\). The sum of all the elements of A is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 22
By the rule, each element is the larger of its row number and column number.
\( \displaystyle A = \begin{bmatrix}1&2&3\\2&2&3\\3&3&3\end{bmatrix} \)
Adding row by row,
\((1 + 2 + 3) + (2 + 2 + 3) + (3 + 3 + 3)\)
\(= 6 + 7 + 9 = 22\)