Thread: 2-dimensional subspace U of C^3.

Can you please Give me an example of a 2-dimensional subspace U of C^3.

thanks

is two dimensional since , which means that is a vector space with two entries.

It's clear that

Now using the definition of subspace:
Since
and is closed under addition and scalar multiplication is a two dimensional subspace of

Thanks for your help. Now how do i

write a basis for this subspace.

Well a basis is any linearly independent that spans the vector space. In the case of , no real constants a,b, will make unless a=b=0. So any ordered pair of real numbers will constitute a basis for

Originally Posted by charikaar

Can you please Give me an example of a 2-dimensional subspace U of C^3.

thanks

Your question is imprecise. First, if is the field , then it is unclear over what field you are considering to be a vector space. For instance it's a 6-dimensional vector space over , but a 3-dimensional one over . You always need to specify the underlying field. Haven, above, assumed that the vector space is over . Check your question!

Question is:
Give an example of a 2-dimensional subspace of


thanks

Noting Bruno's comment on fields. If we assume is an vector space, then my above answer is correct. However if we view as a vector space. Then an example of a two-dimensional vector space would be

I assume based on the vagueness of the question that you are in a Linear Algebra class and you have little or no understanding of what a field is (in the context of the class). So the interpretation of as an vector space, is probably the desired one.