Answered

Westonci.ca makes finding answers easy, with a community of experts ready to provide you with the information you seek. Get quick and reliable solutions to your questions from knowledgeable professionals on our comprehensive Q&A platform. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.

let h be the set of polynomial functions divisible by (x-2) . proof that h is a subspace of vector space of polynomials. show that the three conditions for a subspace are satisficed.

Sagot :

contexto1019

To prove that the set of polynomial functions divisible by (x-2) is a subspace of the vector space of polynomials h, we need to show that it satisfies the three conditions for a subspace:

  1. The set must contain the zero vector. In this case, the zero vector is the polynomial function 0, which is clearly divisible by (x-2). Therefore, this condition is satisfied.
  2. The set must be closed under addition. This means that if f(x) and g(x) are both elements of the set (i.e. they are both polynomial functions divisible by (x-2)), then their sum f(x) + g(x) must also be an element of the set. Since the sum of two polynomial functions divisible by (x-2) is also divisible by (x-2), this condition is satisfied.
  3. The set must be closed under scalar multiplication. This means that if f(x) is an element of the set and k is a scalar, then the product kf(x) must also be an element of the set. Since the product of a polynomial function is divisible by (x-2) and a scalar is also divisible by (x-2), this condition is satisfied.

Therefore, since the set of polynomial functions divisible by (x-2) satisfies all three conditions for a subspace, h is indeed a subspace of the vector space of polynomials.

Learn more about polynomial functions here:

https://brainly.com/question/24380382

#SPJ4

Thank you for your visit. We are dedicated to helping you find the information you need, whenever you need it. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.