Question

若a1,a2,a3,a4线性无关,则秩（a1+a2,a2+a3,a3+a4,a4+a1)

Answer 1

(a1+a2,a2+a3,a3+a4,a4+a1) = (a1,a2,a3,a4)K

K =

1 0 0 1

1 1 0 0

0 1 1 0

0 0 1 1

因为 a1,a2,a3,a4 线性无关

所以 r(a1+a2,a2+a3,a3+a4,a4+a1) = r(K) = 3.