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.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![5. For two 2 × 3 real matrices A = [ai,j], B = [bi,j] € Mat(2 × 3, R), define
d(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). 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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff2e948f6-fd6f-485f-942e-c931230f8579%2Fe75e5537-ca94-4823-b07c-28ccb67fff36%2Fzh8dpn9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:5. For two 2 × 3 real matrices A = [ai,j], B = [bi,j] € Mat(2 × 3, R), define
d(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). 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.
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