Linear Algebra Vector Space Help Needed

[fair mulch]

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[jagged copper]

try to reach an element not in the set from the elements in the set and the operations provided

if you can do that, it’s not a vector space

i believe you should also check for additive inverses?

[shy flame]

How would I prove it's true?

[jagged copper]

make sure all the axioms are satisfied

i don’t think the first one is true because 0 is not a polynomial of odd degree

but i could be wrong

[shy flame]

The zero polynomial must be in the set for it to be a vector space. However, the zero polynomial is of even degree (or sometimes considered as having no degree), and it does not satisfy the requirement of being an odd-degree polynomial. Therefore, the set lacks the zero element...?

[jagged copper]

sounds correct

also, i think scalar multiplication on 0*x = 0 would fail it as well

[shy flame]

+close