Say whether the following sets are vector subspaces of the vector space V in each of the following cases: 1) S1 = {(x, y) ∈ R 2 : |x| = |y|} , V = R 2

Question

Say whether the following sets are vector subspaces of the vector space V in each of the following cases: 1) S1 = {(x, y) ∈ R 2 : |x| = |y|} , V = R 2
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Solution 1

To determine if a set is a subspace of a vector space, it must satisfy three conditions:

  1. The zero vector of the larger vector space is in the set.
  2. The set is closed under vector addition.
  3. The set is closed under scalar multiplication.

Let's check these conditions for the set S1 = {(x Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.

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