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3. Let V1 and V2 be subspaces of R" (over R) Their intersection V=V,nV, is the set of 2 all vectors that lie both in Vị and in V2. Show that V is a subspace of R".

3. Let V1 and V2 be subspaces of R" (over R) Their intersection V=V,nV, is the set of 2 all vectors that lie both in Vị and in V2. Show that V is a subspace of R".

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Problem 3:** Let \( V_1 \) and \( V_2 \) be subspaces of \( \mathbb{R}^n \) (over \( \mathbb{R} \)). Their intersection \( V = V_1 \cap V_2 \) is the set of all vectors that lie both in \( V_1 \) and in \( V_2 \). Show that \( V \) is a subspace of \( \mathbb{R}^n \).
Transcribed Image Text:**Problem 3:** Let \( V_1 \) and \( V_2 \) be subspaces of \( \mathbb{R}^n \) (over \( \mathbb{R} \)). Their intersection \( V = V_1 \cap V_2 \) is the set of all vectors that lie both in \( V_1 \) and in \( V_2 \). Show that \( V \) is a subspace of \( \mathbb{R}^n \).
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