设有向量组a1=(1,1,0)T,a2=(2,3,0)T,a3=(3,1,1)T,a4=(1,-1,2)T,A是三阶矩阵,且有Aa(i)=ia(i+1),括号内为下标,i=1,2,3,试求Aa4.

Question

设有向量组a1=(1,1,0)T,a2=(2,3,0)T,a3=(3,1,1)T,a4=(1,-1,2)T,A是三阶矩阵,且有Aa(i)=ia(i+1),括号
内为下标,i=1,2,3,试求Aa4.

Answer 1

(a1,a2,a3,a4)=
1 2 3 1
1 3 1 -1
0 0 1 2
r2-r1
1 2 3 1
0 1 -2 -2
0 0 1 2
r1-2r2-3r3,r2+2r3
1 0 0 -9
0 1 0 2
0 0 1 2
所以 a4=-9a1+2a2+2a3
所以 Aa4=-9Aa1+2Aa2+2Aa3=-9a2+4a3+6a4=(0,-29,16)^T.