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. Let A be a skew-symmetric matrix, `B= (I-A) (I+A)^(-1)` and X and Y be column vectors conformable for multiplication with B. Statement-1 (BX)^(T) (BY) = X^(T) Y Statement- 2 If A is skew-symmetric, then (I+A) is non-singular.A. Statement- is true, Statement -2 is true, Statement-2 is a correct explanation for Statement-5B. Statement-1 is true, Statement-2 is true, Sttatement - 2 is not a correct explanation for Stamtement-5C. Statement 1 is true, Statement - 2 is falseD. Statement-1 is false, Statement-2 is true

Statement-1 (Assertion and Statement- 2 (Reason) Each of these questio

1.	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. Let A be a skew-symmetric matrix, `B= (I-A) (I+A)^(-1)` and X and Y be column vectors conformable for multiplication with B. Statement-1 (BX)^(T) (BY) = X^(T) Y Statement- 2 If A is skew-symmetric, then (I+A) is non-singular.A. Statement- is true, Statement -2 is true, Statement-2 is a correct explanation for Statement-5B. Statement-1 is true, Statement-2 is true, Sttatement - 2 is not a correct explanation for Stamtement-5C. Statement 1 is true, Statement - 2 is falseD. Statement-1 is false, Statement-2 is true
Answer» Correct Answer - A `because (BX)^(T)(BY) = {(I-A)(+A)^(-1) X}^(T) (I-A) (I+A)^(-1) Y` `=X^(T){(I+A)^(-1) }^(T) (I-A)^(T)(I-A) (I+A)^(-1) Y` `= X^(T)(I+A^(T))^(-1) (I-A^(T))(I-A) (I+A)^(-1) Y` `= X^(T)(I+A)^(-1) (I+A)(I-A) (I+A)^(-1) Y` `= X^(T)(I+A)^(-1) (I-A)(I+A) (I+A)^(-1) Y` `[because A^(T) = - A and (I-A) (I+A) = (I+A) (I-A)]` `=X^(T) cdot Icdot IcdotIY=X^TY` Both Statements are true, Statement-2 is correct explanation for Statement-1.

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