Please help! Let V be an n-dimensional vector space over an infinite field F ansuppose that S1,..., Sk are subspaces of V with dim(S;) <that there is a subspace T of V of dimension n- m forTN S; = {0} for all i.m < n. Prove

Answered: Let V be an n-dimensional vector space…

Principles Of Marketing

17th Edition

ISBN:9780134492513

Author:Kotler, Philip, Armstrong, Gary (gary M.)

Publisher:Kotler, Philip, Armstrong, Gary (gary M.)

Chapter1: Marketing: Creating Customer Value And Engagement

Section: Chapter Questions

Problem 1.1DQ

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Let V be an n-dimensional vector space over an infinite field F an
suppose that S1,..., Sk are subspaces of V with dim(S;) <
that there is a subspace T of V of dimension n- m for
TN S; = {0} for all i.
m < n. Prove

Expert Solution

Step 1

A vector space of $n$ -dimensional has $n$ elements in its basis.

Let the vector space $V$ has the basis of $n$ elements say $\{v_{1}, v_{2}, v_{3}, \dots, v_{n}\}$ .

The dimension of the subspaces of the vector space $V$ is $\dim (S_{i}) \leq m < n$ so let the basis for the subspaces is $\{v_{1}, v_{2}, v_{3}, \dots, v_{m}\}$ .

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