Question

>>>B is a n x m matrix.<<<
a) Prove that if u is in the column space of B and v is in the left null space of B, then u and v are perpendicular.
b) Prove that if x is in the row space of B and y is in the null space of B, then x and y are perpendicular.

Answer 1

what i know so far: B: n x m. Col(B) is a subspace of R^n. Left null space(B)= Null(B's transpose), and N(B) is a subapce of R^n as well.

Answer 2

solved~