求证（t*a）*b=t*(a*b)=a*(t*b)

题目

求证（t*a）*b=t*(a*b)=a*(t*b)

答案

I suppose a,b are vector, t is scaler
let a, b be nth dimensional vector
a = (x1,x2,.,xn)
b = (y1,y2,.,yn)
(ta).b = (tx1,tx2,.,txn).(y1,y2,yn)
= t(x1y1+x2y2+..+xnyn)
a.(tb) = (x1,x2,..,xn). ( (ty1,ty2,.,tyn)
= t(x1y1+x2y2+...+xnyn) = (ta).b