- #1
sjmacewan
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We're working on vector spaces right now and this one problem is iving me a bit of trouble.
Is the following a vector space?
The set of all polynomials of the form [tex]n_2x^2 + n_1x + n_0[/tex]
where [tex]n_0,n_1,n_2 \epsilon Z [/tex](integers)Now I'm pretty sure that this is going to end up NOT being a vector space, by using the properties that we were given (too vague and numerous to list here) But I'm not entirely sure why. I know that when it's an element of the REALS as opposed to the INTEGERS it is a vector space, but i just don't know where to start in this case :(
Is the following a vector space?
The set of all polynomials of the form [tex]n_2x^2 + n_1x + n_0[/tex]
where [tex]n_0,n_1,n_2 \epsilon Z [/tex](integers)Now I'm pretty sure that this is going to end up NOT being a vector space, by using the properties that we were given (too vague and numerous to list here) But I'm not entirely sure why. I know that when it's an element of the REALS as opposed to the INTEGERS it is a vector space, but i just don't know where to start in this case :(
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