How do I check if this is a subspace of R2?

[spring mauve]

I know that linear algebra does not deal with any exponent and this is probably not a subspace but I am not sure how to prove this.

[tame grove]

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[midnight kraken]

just check the definition of being a subspace

[spring mauve]

that doesn't really answer anything

it's like saying "just google it"

[midnight kraken]

it very much answers your question

a set is a subspace if it meets the definition

so check whether all the conditions hold or not

is in the set?
if u,v are in the set, is u+v?
if u is in the set and a is a scalar, is au in the set?

[cyan ginkgo]

Wait

What does that exponentiation even mean?

I don't even understand what the set means

The set of all vectors such that x1^2 = x2^3 ??

What does this mean

What is x1,x2 and how can you multiply vectors??

[midnight kraken]

x=[x1,x2]

[cyan ginkgo]

Ahhhh

ok

Let me see if it's a subspace now

a a real scalar and x a vector then ax = a*(x1, x1^(2/3)) = (ax1, a^(1/3) * (ax)^(2/3))

so nah

It's not a subspace