Question

1. Let and be subspaces of . Prove that $U\cap W$ is also a subspace of .

Answer 1

Solution;

Given that;

Given data: - U and w are subspaces v implies 0 elementof U, 0 elementof w implies 0 elementof U intersection w implies U intersection w is non empty subset of 'v' Assume Let x, y elementof U intersection w, a, b elementof F implies x, y elementof U and x, y elementof w implies x, y elementof w, a, b elementof w, a, b elementof Fw is a subspace of v then ax + by elementof v implies x, y elementof w, a, b elementof Fw is a subspace of v then ax + by elementof w Here implies ax + by elementof U intersection w There fore U intersection w is subspace of v