Question

若向量组a1={1,-1,2},a2={2,-1,3},a3={2,3,k},a4={-2,0,2k}的秩为2,求k的值

Answer 1

a1,a2 is linearly independent
a3 = k1a1+k2a2
=>
2= k1+2k2 (1) and
3=-k1-k2 (2) and
k=2k1+3k2 (3)
(1)+(2)
k2=5,
k1=-8
from (3)
k=2(-8)+3(5)=-1