[Solved] MATH307 Individual Homework13

Instructions: Read textbook pages 65 to 67 before working on the homework problems. Show all steps to get full credits.

1. Let Q be an arbitrary unitary matrix of size 33,

1 3 x = 2 ,y = 0 ,

3 1

find the angle between Qx and Qy.

2. Prove that the null space of A F^mn is a subspace of Fⁿ.
3. Let

1 2

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.