Statement I: A matrix $A = {(a_{i j})}_{3 \times 3}$ such that $a_{i j} = \frac{i - j}{\hat{i} + 2 \hat{j}}$ cannot be expressed as sum of symmetric and skew symmetric matrix
Statement 2: A matrix = ${(a_{i j})}_{3 \times 3}$ such that $a_{i j} = \frac{i - j}{\hat{i} + 2 \hat{j}}$ neither symmetric (nor) skew symmetric

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Statement I is false Statement 2 is true

Both Statements are true and statement 2 is correct explanation of statement I

Statement I is true and statement 2 is false

Both statement are true but statement 2 is not a correct explanation of statement I

answer is D.

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Detailed Solution

$A = (a_{i j}) = \frac{i - j}{i + 2 j} = (\begin{matrix} 0 & - \frac{1}{5} & - \frac{2}{7} \\ \frac{1}{4} & 0 & - \frac{1}{8} \\ \frac{2}{5} & \frac{1}{7} & 0 \end{matrix}) i s$ neither symmetric nor skew symmetric but every square matrix can be expressed sum of symmetric and skew symmetric