PROBLEM 3: Consider the set s={A€M₂x3 (P (R): A = 0 с ab 0 , where a > 0, b>0, >>o, c>0}. with the usual matrix addition and matrix scalar multiplication. a) Give an example of an element in S. b) Show that S is closed under addition or give an example to show that it's not. c) Show that S is closed under scalar multiplication or give an example to show that it's not. d) Find a basis for S. Make sure to verify the requirements for a basis. e) Find dim[S].

PROBLEM 3: Consider the set s={A€M₂x3 (P (R): A = 0 с ab 0 , where a > 0, b>0, >>o, c>0}. with the usual matrix addition and matrix scalar multiplication. a) Give an example of an element in S. b) Show that S is closed under addition or give an example to show that it's not. c) Show that S is closed under scalar multiplication or give an example to show that it's not. d) Find a basis for S. Make sure to verify the requirements for a basis. e) Find dim[S].

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.2: Linear Independence, Basis, And Dimension

Problem 5AEXP

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Take this test to review the material in Chapters 4 and 5. After you are finished, check your work against the answers in the back of the book. Determine whether the columns of matrix A span R4. A=[1210130200111001]

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