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1. The set of 2 x 2 matrices with real number entries, denoted M2(R) : a, b, c, d e R}, is a vector space over R. Give two concrete examples of vectors in this vector space. Give two concrete examples of scalars in this vector space. What is the zero vector in this vector space? Verify the commutativity of addition property for this vector space by showing that tU =0+ u for u, v E M2(R). (e) Give a basis for this vector space. Is this vector space finite dimensional or infinite dimensional? If it is finite dimensional, what is the dimension?

1. The set of 2 x 2 matrices with real number entries, denoted M2(R) : a, b, c, d e R}, is a vector space over R. Give two concrete examples of vectors in this vector space. Give two concrete examples of scalars in this vector space. What is the zero vector in this vector space? Verify the commutativity of addition property for this vector space by showing that tU =0+ u for u, v E M2(R). (e) Give a basis for this vector space. Is this vector space finite dimensional or infinite dimensional? If it is finite dimensional, what is the dimension?

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.6: The Matrix Of A Linear Transformation
Problem 7AEXP
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1. The set of 2 x 2 matrices with real number entries, denoted M2(R) : a, b, c, d e R}, is a vector space over R. Give two concrete examples of vectors in this vector space. Give two concrete examples of scalars in this vector space. What is the zero vector in this vector space? Verify the commutativity of addition property for this vector space by showing that tU =0+ u for u, v E M2(R). (e) Give a basis for this vector space. Is this vector space finite dimensional or infinite dimensional? If it is finite dimensional, what is the dimension?
Transcribed Image Text:1. The set of 2 x 2 matrices with real number entries, denoted M2(R) : a, b, c, d e R}, is a vector space over R. Give two concrete examples of vectors in this vector space. Give two concrete examples of scalars in this vector space. What is the zero vector in this vector space? Verify the commutativity of addition property for this vector space by showing that tU =0+ u for u, v E M2(R). (e) Give a basis for this vector space. Is this vector space finite dimensional or infinite dimensional? If it is finite dimensional, what is the dimension?
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