Homepage › Solution manuals › Sheldon Axler › Linear Algebra Done Right › Exercise 3.E.7

Linear Algebra Done Right

Exercise 3.E.7

Answers

$\forall u \in U$

\begin{matrix} \begin{aligned} (v - x) + U & = W \\ (v - x) + u & \in W \end{aligned} \end{matrix}

(1)

Since $(v - x) \in W$ (by setting $u = 0$ )

u \in W

We can repeat this process to prove that

w \in U

Proving that $U = W$ □

Arden_Shi

2025-06-01 23:14

Comments