试将向量b=(1,2,1)^T表示成向量组a1=(1,-1,1)^T,a2=(1,1,-1)^t,a3=(1,1,1)^t的线性组合.怎么解?谢谢!
问题描述:
试将向量b=(1,2,1)^T表示成向量组a1=(1,-1,1)^T,a2=(1,1,-1)^t,a3=(1,1,1)^t的线性组合.怎么解?谢谢!
答
(a1,a2,a3,b)=
1 1 1 1
-1 1 1 2
1 -1 1 1
r2+r1,r3-r1
1 1 1 1
0 2 2 3
0 -2 0 0
r2+r3,r3*(-1),r1-r3
1 0 1 1
0 0 2 3
0 1 0 0
r2*(1/2),r1-r2
1 0 0 -1/2
0 0 1 3/2
0 1 0 0
r2r3
1 0 0 -1/2
0 1 0 0
0 0 1 3/2
b = -(1/2)a1+0a2+(3/2)a3.