5. For two 2 × 3 real matrices A = [ai,j], B = [bi,j] € Mat(2 × 3, R), defined(A, B) := max{|ai,j — bi,j| : i = 1, 2, j = 1, 2, 3}(a). Show that d is a metric on Mat(2 × 3, R).(b). LetX = {A E Mat(2 × 3, R) : rows of A are linearly indepedent}Show that X is an open subset of Mat(2 × 3, R) under the metric d.

Answered: Image /qna-images/answer/e75e5537-ca94-4823-b07c-28ccb67fff36.jpg

5. For two 2 × 3 real matrices A = [ai,j], B = [bi,j] € Mat(2 × 3, R), define d(A, B) :: := max{|ai,j - bij|: i = 1, 2, j = 1, 2, 3} (a). Show that d is a metric on Mat (2 x 3, R). (b). Let X = {A E Mat(2 × 3, R): rows of A are linearly indepedent Show that X is an open subset of Mat(2 × 3, R) under the metric d.

5. For two 2 × 3 real matrices A = [ai,j], B = [bi,j] € Mat(2 × 3, R), define d(A, B) :: := max{|ai,j - bij|: i = 1, 2, j = 1, 2, 3} (a). Show that d is a metric on Mat (2 x 3, R). (b). Let X = {A E Mat(2 × 3, R): rows of A are linearly indepedent Show that X is an open subset of Mat(2 × 3, R) under the metric d.

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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