MATH307-Individual Homework 13 Solved

1.   Let Q be an arbitrary unitary matrix of size 3×3,

Ñ1é Ñ−3é x = 2 ,y = 0 ,

                                                                                        3                       1

find the angle between Qx and Qy.

2.   Prove that the null space of A ∈ Fm×n is a subspace of Fn.

3.   Let

Å1 2ã

                                                                                        A =                  ,

1 2

find a basis for its range range(A).

4.   Prove range(AB) ⊆ range(A) for appropriate A,B that could be multiplied together.