Given the set of linear equations:

a11 x1 + a12 x2 + a13 x3 = 0

a22 x2 + a23 x3 = 0

a33 x3 = 0

assume D = 0 (determinant), this implies that at least 1 of a22 or a33 is 0. show if x !=0 then D != 0

My try:

when I do D I get -> (a11 a22 a33), but if a22 or a33 is 0, then D=0. So I'm not sure what is going on here as if a33 = 0 then x3 can be anything, implying x!=0?