Answered: Let V be the vector space of all (3×3)…

Let V be the vector space of all (3×3) matrices and W be the set of all (3×3) matrices A for which A2 = A. Determine whether W is a subspace of V .

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.1: Vector Spaces And Subspaces

Problem 30EQ: In Exercises 24-45, use Theorem 6.2 to determine whether W is a subspace of V. V=Mnn,WAinMnn:detA=1

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Question

Let V be the vector space of all (3×3) matrices and W be the set of all (3×3) matrices
A for which A² = A. Determine whether W is a subspace of V .

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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