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I'm trying to learn linear algebra on my own. I'm a freshman, blah blah, who really cares, now to the math :)

1) Prove that if (v1,v2,v3) span V, then (v1 + 2v2, v2 - v3, v3) also span V

2)Prove that if (v1,v2,v3) is linearly independent, then (v1 + 2v2, v2 - v3, v3) is also linearly independent

3) let P(|F) be the space of polynomials with coefficients in |F

(i) Find two different subspaces of P(|F)

(ii) Find an infinite dimensional proper subspace of P(|F)

4) Let U,V be subspaces of F^7, such that U and the direct sum of V = F^7. if dim U=3, show that dim V=4.

(ii) does this remain true if all we know is that U+V=F^7 ?

i'm new at this, i've been reading the textbooks and what have you, but i'm not seeing the answers.

thx

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# Homework Help: Trying to learn linear algebra on my own

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