let $W_1, W_2$ and $W_3$ be subspaces of $V$

Let $V=\mathbb R^2$ and $$W_1=\{(x,y)\in V:x=y\}$$ $$W_2=\{(x,y)\in V:x=0\}$$ $$W_3=\{(x,y)\in V: y=0\}$$

Then $W_1 \cap (W_2 +W_3)$ is equal ______?

My attempt:
$W_1 \cap (W_2 +W_3)= (x,x) \cap \{(x,0) +(0,y)\}=(x,x) \cap(x,y) =(x,x)$

Is it correct?

Any hints/solution?

Thank you!


Yes, the heuristic is good.
You only have to prove that $W_2+W_3=\Bbb R^2$, then $W_1\cap(W_2+W_3)=W_1$ immediately follows.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.