Exercise 4.3.29

Only 1 plane contains $0,a_1,a_2$ unless $a_1,a_2$ are dependent. Same test for $a_1,\dots ,a_{n-1}$. If they are dependent, there is a vector $v$ perpendicular to all the $a$ ’s. Then they all lie on the plane $v^{T}x=0$ going through $x=(0,0,\dots ,0)$.