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
Solution 1
To determine if a set is a subspace of a vector space, it must satisfy three conditions:
- The zero vector of the larger vector space is in the set.
- The set is closed under vector addition.
- 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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