An n-vector x is symmetric if Xk-X,ã¼k+1 for k = 1 , . . . , n. It is anti-symmetric if Xk =-x,'-k+1 for (a) Show that every vector x can be decomposed in a unique way as sumx-X a of a symmetric vector r and an anti-symmetric vectora b) Show that the symmetric and anti-symmetric parts x, and and A, such that X,=Arx, and xa=Arx for all are linear functions of x. Given matrices A,
