If A= [ array ccc 2 & 0 & -3 4 & 3 & 1 -5 & 7 & 2 array ] is expressed as a sun of a symmetric matrix P and skew symmetric matrix Q , then P ^ T - Q ^ T =

Step-by-step solution

Given : A= [ array ccc 2 & 0 & -3 4 & 3 & 1 -5 & 7 & 2 array ] Since, each and every matrix can be written as sum of symmetric & skew symmetric matrix. A can be written as sum symmetric matrix P and skew symmetric matrix Q. where P = 1 2 [ ~A + A ^ T ] Q = 1 2 [ ~A - A ^ T ] aligned & Now, A^T= [ array ccc 2 & 4 & -5 0 & 3 & 7 -3 & 1 & 2 array ] & P= 1 2 [ array ccc 4 & 4 & -8 4 & 6 & 8 -8 & 8 & 4 array ]= [ array ccc 2 & 2 & -4 2 & 3 & 4 -4 & 4 & 2 array ] & Q= 1 2 [ array ccc 0 & -4 & 2 4 & 0 & -6 -2 & 6 & 0 arra