Q03.Let V be an n-dimensional vector space over F, with n 2 1. Let B = {°v1, . ,*Vn}be a basis of V.1. (а)2. (b)Let *x E V. Prove that if ["x]B = Of», then *x = "0v.Let S be a subspace of V, let C={w1..,w°k}be a basis of S, and let T={[°v]p:°V€S}be a subspace of F". Prove that dim T = k.

Given : V be an n-dimensional vector space over F, with n≥1 and B = v1, v2, ..., vn be a basis of V.…

Answered: Q03. be a basis of V. Let V be an…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Q03. be a basis of V. Let V be an n-dimensional vector space over F, with n ≥ 1. Let B = {v₁,..., Vn} 1. (a) Let *x € V. Prove that if [x]B="0F, then "x = "0y. 2. (b) Let S be a subspace of V, let C={w 1..w k}be a basis of S, and let T={[v]B:"VES} be a subspace of Fn. Prove that dim T = k.