## Elementary Linear Algebra 7th Edition

Published by Cengage Learning

# Chapter 4 - Vector Spaces - 4.3 Subspaces of Vector Spaces - 4.3 Exercises - Page 167: 30

#### Answer

The set W of all $n\times n$ diagonal matrices is a vector subspace of $M_{n,n}$.

#### Work Step by Step

The set W of all $n\times n$ diagonal matrices is a vector subspace of $M_{n,n}$. Because the sum of two diagonal matrices is a diagonal matrix and multiplying any diagonal matrix by a constant is a diagonal matrix which means that W is closed under addition and scalar multiplication.

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