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

To determine whether the set $S_1 = \{(x, y) \in \mathbb{R}^2 : |x| = |y|\}$ is a vector subspace of the vector space $V = \mathbb{R}^2$, we will check two main criteria for a subset to be a subspace:

1. Non-emptiness/Contains the Zero Vector
2. **Closure under Addition and Scalar Mult Knowee AI is a powerful AI-powered study tool designed to help you to solve study problem.