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2. Let M be the collection of all 2 × 2 real matrices. If define a b ^ - (**) EM A= C d |A| = and max(|A|) = max{|a|, |b|, |c|, |d|}. For A, B E M, define Show that (M, d) is a metric space. |a| b| │c| |d| d(A, B) := max{|A – B|}

2. Let M be the collection of all 2 × 2 real matrices. If define a b ^ - (**) EM A= C d |A| = and max(|A|) = max{|a|, |b|, |c|, |d|}. For A, B E M, define Show that (M, d) is a metric space. |a| b| │c| |d| d(A, B) := max{|A – B|}

Advanced Engineering Mathematics
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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2. Let M be the collection of all 2 × 2 real matrices. If define a b ^- (^ ^) M A= E C d |A| = and max(|A|) = max{|a], [b], [c], |d|}. For A, B E M, define Show that (M, d) is a metric space. |a| b| │c| |d| d(A, B) := max{|A – B|}
Transcribed Image Text:2. Let M be the collection of all 2 × 2 real matrices. If define a b ^- (^ ^) M A= E C d |A| = and max(|A|) = max{|a], [b], [c], |d|}. For A, B E M, define Show that (M, d) is a metric space. |a| b| │c| |d| d(A, B) := max{|A – B|}
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