If `B-A^(T)={:[(3,4,-2),(5,-3,7)]:}andB^(T)+A={:[(2,0),(5,-1),(3,4)]:}`, then find Matrix A.

Options

A. `{:[(1//2,-3//2),(1//2,1),(-5//2,3//2)]:}`
B. `{:[(1//2,3//2),(1//2,1),(-5//2,3//2)]:}`
C. `{:[(-1//2,-5//2),(1//2,1),(5//2,-3//2)]:}`
D. `{:[(1//2,3//2),(1//2,1),(-5//2,3//2)]:}`

Answer

C

Explanation

(i) Transpose `B^(T)+A={:[(2,0),(5,-1),(3,4)]:}` and add it to the other equation.
(ii) `(B-A^(T))^(T)=B^(T)-A`.
(iii) Subtract `(B^(T)-A)" from "B^(T)+A`.