Question

Statement-1 (Assertion and Statement- 2 (Reason)
Each of these questions also has four alternative
choices, only one of which is the correct answer. You
have to select the correct choice as given below.
Statement - 1 `A=[a_(ij)]` be a matrix of order `3xx3` where
`a_(ij) = (i-j)/(i+2j)` cannot be expressed as a sum of symmetric
and skew-symmetric matrix.
Statement-2 Matrix `A= [a_(ij)] _(nxxn),a_(ij) = (i-j)/(i+2j) ` is neither
symmetric nor skew-symmetric.
A. Statement- is true, Statement -2 is true, Statement-2
is a correct explanation for Statement-1
B. Statement-1 is true, Statement-2 is true, Sttatement - 2
is not a correct explanation for Stamtement-1
C. Statement 1 is true, Statement - 2 is false
D. Statement-1 is false, Statement-2 is true

Answer 1

Correct Answer - D
`A= [[0, -1/5, -2/7],[1/4, 0 , -1/8],[2/5, 1/7, 0]]`
which is neither symmetric nor skew-symmetric. Infact every
square matrix can be expressed as a sum of symmetric and
skew-symmetric matrix. Hence, Statement-1 is false and
Statement -2 is true.