Question

设α1=(1,0,2),α2=(2,0,-3),α3=(1,2,1),任一向量β=(a,b,c)能否由α1,α2,α3线

Answer 1

可以.

β=(a,b,c)

设β=Aα1 + Bα2 + Cα3

则a = A + 2B + C

b = 2C

c = 2A - 3B + C

由上解得C = b/2

B = (4a-2c-b)/14

A = (6a-5b+4c)/14

所以可以用α1,α2,α3来表示β.