(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

x belongs to the vector space R^6.

Is (x1-x2)^4 + x3^6 = 0 a subspace?

2. Relevant equations

Since we already know x is a vector space we only need to check:

1. The existence of the zero vector

2. Closure under vector addition

3. Closure under scalar addition

3. The attempt at a solution

1.(0,0,0) = 0 √ check

2.x = (-4,-4,0), y = (3,3,0)

x+y = (-1,-1,0) satisfies equation √ check

3.-1*(2,2,0) = (-2,-2,0) satisfies equation √ check

All of this seems straightforward, I'm just having a real problem with the exponents in the expression. I know that vector spaces deal with linear combinations of vectors. Does it matter that the expression of the subspace itself is not linear?

Does that somehow change the rules or can a subspace be any crazy function we want? (as long as it consists of vectors and scalars)

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# Homework Help: Is the following set a subspace?

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