Answered: 18. Let Q denote the set of all (2 x 2)…

18. Let Q denote the set of all (2 x 2) singular matrices with the usual matrix addition and scalar multipli- cation. Determine whether Q is a vector space.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.2: Norms And Distance Functions

Problem 33EQ

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Question

Linear algebra: please solve q18 correctly and handwritten

erty (c1) of Definition 1. Also show that properties
(c2) and (a3) are not met.
18. Let Q denote the set of all (2 x 2) singular matrices
with the usual matrix addition and scalar multipli-
cation. Determine whether Q is a vector space.
1
22 Prove property 3 of Theorem 1
of
Hint: Note that

Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.

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