AkilMAI said:Homework Statement
How can I find the base and dim of U here?, V = P3; U = {p in P3 : p'(0) = p(1)}...
Homework Equations
The Attempt at a Solution
now I've proven it is a subspace and that it is closed under addition and scalar multiplication...but how can I find the base and dim?I was thinking about writing it as p(x)=a+bx+cx^2+dx^4=>p(x)'=b+2cx+3dx^2
and...p'(0)=p(1)=>b=a+b+c+d=>d=-a-c...
Thank you
A subset of a vector space is a collection of vectors that are contained within the original vector space. This means that all of the vectors in the subset can be added and scaled by the same scalar values as the original vectors in the vector space.
To determine if a set of vectors is a subset of a vector space, you can check if the set satisfies the three fundamental properties of a vector space: closure under vector addition, closure under scalar multiplication, and the existence of a zero vector. If the set satisfies all three properties, then it is a subset of the vector space.
Yes, a subset of a vector space can be a vector space itself as long as it satisfies the three fundamental properties mentioned above. However, it may not have the same dimension as the original vector space.
To prove that a set is a subset of a vector space, you can use the definition of a subset and show that all of the elements in the set also belong to the vector space. This can be done by checking if the elements satisfy the three fundamental properties of a vector space.
Yes, a subset of a vector space can contain an infinite number of vectors. For example, the set of all real numbers is a subset of the vector space of all complex numbers, which contains infinitely many vectors.