Answered: Suppose V,W are subspaces of R^n. Let V…

Suppose V,W are subspaces of R^n. Let V ∩ W be all vectors which are in both V and W. Show that V ∩W is a subspace also.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section3.5: Subspaces, Basis, Dimension, And Rank

Problem 10EQ

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Question

Suppose V,W are subspaces of R^n. Let V ∩ W be all vectors which are in both V and
W. Show that V ∩W is a subspace also.

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

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