Let A be a 2 by 3 matrix whose rows, v1 and v2 are nonzero, nonparallel vectors in R3. Why is any nonzero vector x that satisfies the equation Ax = 0 a normal vector for the plane spanned by the vectors v1 and v2?
Suppose E is a 3 by 5 matrix and F is a 5 by 3 matrix. Why is it not possible for the matrices to commute? That is, why cannot EF equal FE?
This post expresses nonzero vectors.