If the matrix [ array rr 2 & 3 5 & -1 array ]=A+B , where A is symmetric and B is skew-symmetric, then B is equal to

Step-by-step solution

Given, [ array rr 2 & 3 5 & -1 array ]=A+B We know that, every square matrix can be expressed uniquely as the sum of symmetric and skew-symmetric matrix. Let C= [ array rr 2 & 3 5 & -1 array ] Since, A is symmetric and B is skew-symmetric matrix. aligned C &= 1 2 (C+C^ )+ 1 2 (C-C^ )=A+B B &= 1 2 (C-C^ )= 1 2 ( array rr 2 & 3 5 & -1 array )- ( array rr 2 & 5 3 & -1 array ) &= 1 2 ( array rr 0 & -2 2 & 0 array )= ( array rr 0 & -1 1 & 0 array ) aligned