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,
x =
Ñ
1
2
3
é
, y =
Ñ
−3
0
1
é
,
find the angle between Qx and Qy.
2. Prove that the null space of A ∈ F
m×n
is a subspace of F
n
.
3. Let
A =
Å
1 2
1 2ã
,
find a basis for its range range(A).
4. Prove range(AB) ⊆ range(A) for appropriate A, B that could be multiplied
together.
