0
$\begingroup$

Vector space is a space consisting of vectors, together with the associative and commutative operation of addition of vectors, and the associative and distributive operation of multiplication of vectors by scalars.

For each $W \subseteq V \ $ if $\ W$ is a vector space itself (which means that it is closed under operations of addition and scalar multiplication), with the same vector space operations as $V$ has, then $W$ is a subspace of $V$.

Question:
Give an example of 3 subspaces of $V$ such that $w_1 \cap (w_2+w_3) \neq (w_1 \cap w_2) + (w_1 \cap w_3)$

Note: I tried everything i could but the two sides are equal in all of my examples ...

Thanks in advance.

$\endgroup$
0
$\begingroup$

Let $V=\mathbb R^2$ and $W_1=[x=y], W_2=[x=0], W_3=[y=0]$.

$\endgroup$

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.