Hello MHF, would appreciate some help with the following equestions;

Determine which of the following sets are subspaces. Give reasons for your answers.

(a)

(b)

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- May 31st 2009, 01:34 AMRobbSubspaces
Hello MHF, would appreciate some help with the following equestions;

Determine which of the following sets are subspaces. Give reasons for your answers.

(a)

(b) - May 31st 2009, 02:20 AMMoo
Hello,

You have to check that for any u,v belonging to the set, u+v belongs to the set, and for any real number , belongs to the set.

Quote:

(a)

Does this belong to ?

Consider the case when

Quote:

(b)

Can the first coordinate be in the form ?

The problem here is that s and t are the same in the first and the second coordinates.

If there weren't, you could have just written

But you would have to get as your second coordinate... - May 31st 2009, 02:26 AMHallsofIvy
A subset of a vector space is a subspace if and only if it is "closed" under vector addition and scalar multiplication.

If u and v are two members of H, they are of the form and for some**positive**numbers s and t. Their sum is while, for any number k, . What happens if k is negative?

If u and v are two members of L, they are of the form and where s, t, x, y can be any real numbers. Their sum is and, for a real number k, . Can you see that those are NOT of the correct form for L? - May 31st 2009, 02:28 AMMoo
To

**Robb**and**HallsOfIvy**: using \begin{bmatrix} ... \end{bmatrix} is shorter than going with arrays :)