Which ones of the following subsets of are subspaces.

a)

b)

c)

d)

I should decide their dimensions and give a basis for each. I think a) and d) are subspaces, how can I find the dimension of these spaces and how can I give a basis?

Thank you!

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- Nov 12th 2011, 10:50 AMgotmejerryAre these subspaces of R^n?
Which ones of the following subsets of are subspaces.

a)

b)

c)

d)

I should decide their dimensions and give a basis for each. I think a) and d) are subspaces, how can I find the dimension of these spaces and how can I give a basis?

Thank you! - Nov 12th 2011, 11:39 AMFernandoRevillaRe: Are these subspaces of R^n?
- Nov 12th 2011, 12:00 PMgotmejerryRe: Are these subspaces of R^n?
I did it this way. So when the linear combination of 2 random elements of the set gives an element which in the set too, it is a subspace.

For c) the 0-vector isn't in the set so it cannot be a subspace.

For d) I did the same what you did with a). It is a subspace.

For b) I got from the lin.comb of 2 elements (a+b)*c when c is the constant and a,b are scalars, so I think I should have got c, so it is not a subspace.

But my main problem is I cannot decide their dimensions and cannot give a basis(Speechless) - Nov 12th 2011, 12:37 PMFernandoRevillaRe: Are these subspaces of R^n?
- Nov 12th 2011, 01:09 PMgotmejerryRe: Are these subspaces of R^n?
My conclusion, its dimension is n-1. What about the d)?

- Nov 12th 2011, 02:48 PMFernandoRevillaRe: Are these subspaces of R^n?
- Nov 12th 2011, 02:54 PMgotmejerryRe: Are these subspaces of R^n?
And are my assumptions correct that b) and c) are not subspaces?

- Nov 12th 2011, 04:03 PMFernandoRevillaRe: Are these subspaces of R^n?