Q44 / 160 · AP EAMCET 2023 (16 May Shift 2) · Mathematics

A matrix whose elements $a_{i j}$ are defined by $a_{i j}=\frac{1}{3}|i-5 j|, i, j=1,2,3 \text { is }$

  • A
    $\left[\begin{array}{ccc}4 & 3 & \frac{14}{3} \\ 1 & \frac{8}{3} & 13 \\ \frac{2}{3} & \frac{7}{3} & 4\end{array}\right]$
  • Correct answer
    B
    $\left[\begin{array}{ccc}\frac{4}{3} & 3 & \frac{14}{3} \\ 1 & \frac{8}{3} & \frac{13}{3} \\ \frac{2}{3} & \frac{7}{3} & 4\end{array}\right]$
  • C
    $\left[\begin{array}{ccc}\frac{4}{3} & 3 & \frac{10}{3} \\ 1 & \frac{8}{3} & \frac{13}{3} \\ 2 & 7 & 4\end{array}\right]$
  • D
    $\left[\begin{array}{lll}4 & 3 & 10 \\ 1 & 8 & 13 \\ 2 & 7 & 4\end{array}\right]$

Solution

The given matrix is defined by $\mathrm{a}_{\hat{\mathrm{ij}}}=\frac{1}{3}|\mathrm{i}-5 \mathrm{j}|$ So, $\left(\begin{array}{lll}a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33}\end{array}\right)=\left(\begin{array}{ccc}\frac{4}{3} & 3 & \frac{14}{3} \\ 1 & \frac{8}{3} & \frac{13}{3} \\ \frac{2}{3} & \frac{7}{3} & 4\end{array}\right)$

Hence, the correct answer is option: 'B'.

Relevant Questions