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1. (Original post by Noble.)
Ah right, so is L+M = R^2?

Am I right in saying L+N is also R^2? So the RHS is R^2 with L on the LHS giving a counter-example?
Correct.

I don't know the definition you've been given, but there may have been slightly easier ways to get L+N=R2. I'm going to take the definition L+N=span(LUN).

Intuitive: You have two non-parallel lines through the origin. You can clearly reach quite a few points by traveling along L followed by a line parallel to N. Thinking for a bit longer you can see that you can actually reach any point this way.

Formal: Unfortunately I've forgotten all the results. Maybe something like if X is a set of linearly independent vectors then X is a basis for span(X), and by definition the dimension is the cardinality of the basis. Then something about the dimension of a proper subspace of a finite dimensional vector space. There could well be something more direct.
2. (Original post by Noble.)
Ah right, so is L+M = R^2?

Am I right in saying L+N is also R^2? So the RHS is R^2 with L on the LHS giving a counter-example?
Yep - as harr said.
3. (Original post by harr)
Correct.

I don't know the definition you've been given, but there may have been slightly easier ways to get L+N=R2. I'm going to take the definition L+N=span(LUN).

Intuitive: You have two non-parallel lines through the origin. You can clearly reach quite a few points by traveling along L followed by a line parallel to N. Thinking for a bit longer you can see that you can actually reach any point this way.

Formal: Unfortunately I've forgotten all the results. Maybe something like if X is a set of linearly independent vectors then X is a basis for span(X), and by definition the dimension is the cardinality of the basis. Then something about the dimension of a proper subspace of a finite dimensional vector space. There could well be something more direct.
Thanks, the definition we use for L+N is

It's quite obvious now you can reach any point in and I'm annoyed I didn't see it earlier - also thinking of L+N to be the span makes it easier to see you can get any point in

(Original post by ghostwalker)
Yep - as harr said.
Thanks a lot, I got there in the end

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