- #1
InbredDummy
- 85
- 0
Waddup everyone
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
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