Question

设a1,a2线形无关,a1-b,a2-b线形相关,证明：存在k1,k2,使得b=k1a1 k2a

Answer 1

a1-b,a2-b线性相关存在c1,c2c1(a1-b)+c2(a2-b) =0 ( c1 or c2不等于0)c1a1+c2a2 = (c1+c2)b b = [c1/(c1+c2)]a1 + [c2/(c1+c2)]a2=>存在 k1 =c1/(c1+c2) , k2 =c2/(c1+c2) stb=k1a1+k2a...