I need some help with examples. Especially number 2.(adsbygoogle = window.adsbygoogle || []).push({});

1) Name a subset which is closed under vector addition and additive inverses but is not a subspace of R squared.

I think I got this one. {(x,y) st x,y are elements of integers} because this isnt closed under scalar multiplication

2) Give an example of a function f: R squared --> R that satisfies f(av) = af(v) for all a in the element of R and all v in the element of R squared, but f is not linear.

I don't really know what a linear function is. I tried f=0V, but my teacher said that's wrong. Any advice?

3) Find a set of 4 linearly independent vectors in the vector space L(R squared, R squared)

I think {3x+1, 4x, 8x^2 - x, 12x^3 - x^2} is an answer.

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# Homework Help: Linear Independence and Linear Functions

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