MATH307 Individual Homework13 Solved

Description

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 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 ∈ F^m×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.