Question

Assertion :Matrix $3\times 3,a_{ij}=\frac{i-j}{i+2j}$ cannot be expressed as a sum of symmetric and skew-symmetric matrix. Reason: Matrix $3\times 3,a_{ij}=\frac{i-j}{i+2j}$ is neither symmetric nor skew-symmetric.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Assertion is incorrect but Reason is correct

Answer 1

The correct option is D Assertion is incorrect but Reason is correct

$a_{ij}=\frac{i-j}{i+2j}\therefore A=\left[\begin{array}{ccc}0& \frac{-1}{5}& \frac{-2}{7}\\ \frac{1}{4}& 0& \frac{-1}{8}\\ \frac{2}{5}& \frac{1}{7}& 0\end{array}\right]$ (Putting corresponding values of $i$ & $j$)

$\therefore A$ can be expressed as a sum of symmetric and asymmetric matrix (True for all matrices)

$A$ is not symmetric or skew-symmetric.