Question

关于正交向量组的一道题目已知三维向量A1=[1 2 3]T,试求非零向量A2,A3,使A1,A2,A3成为正交向量组

Answer 1

设x=(x1,x2,x3)^T 与 A1正交.

则 x1+2x2+3x3 = 0

得基础解系 b1 = (-2,1,0)^T,b2=(-3,0,1)^T

将 b1,b2 正交化:

c1 = b1

c2 = b2 - (6/5)b1 = (1/5)(-3,-6,5)^T

则 A2 = c1 = (-2,1,0)^T

A3 = (3,6,-5)^T

即为所求.