- #1
realcomfy
- 12
- 0
I have a quick question about vector spaces.
Consider the vector space of all polynomials of degree < 1. If the leading coefficient (the number that multiplies [tex]x^{N-1}[/tex]) is 1, does the set still constitute a vector space?
I am thinking that it doesn't because the coefficient multiplying [tex]x^{N-1}[/tex] is the same as the coefficient multiplying [tex]x^{0} = 1[/tex], and then it would not be linearly independent, or something like that, but I am not totally sure about this. Any clarification would be greatly appreciated.
Consider the vector space of all polynomials of degree < 1. If the leading coefficient (the number that multiplies [tex]x^{N-1}[/tex]) is 1, does the set still constitute a vector space?
I am thinking that it doesn't because the coefficient multiplying [tex]x^{N-1}[/tex] is the same as the coefficient multiplying [tex]x^{0} = 1[/tex], and then it would not be linearly independent, or something like that, but I am not totally sure about this. Any clarification would be greatly appreciated.