Question

Let $A=[a_{ij}{]}_{3\times 3}$ be a matrix such that $a_{ij}=\{\begin{array}{ccc}|i-j|,& & i>j\\ 2i+j,& & i\le j\end{array}.$ Then the value of $a_{13}+a_{31}$ is

[1 mark]

• A. $5$
• B. $2$
• C. $3$
• D. $7$

Answer 1

The correct option is D $7$

Given : $a_{ij}=\{\begin{array}{ccc}|i-j|,& & i>j\\ 2i+j,& & i\le j\end{array}$

If $i>j,$ then $a_{ij}=|i-j|$
$\Rightarrow a_{31}=|3-1|=2$

If $i\le j,$ then $a_{ij}=2i+j$
$\Rightarrow a_{13}=2\times 1+3=5$
$\therefore a_{13}+a_{31}=5+2=7$