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Problem 25. A square matrix is a diagonal if aij = 0 whenever i j. a) If A is diagonal, prove that A is diagonal, in fact, how is AT related to A b) If A, B are diagonal, prove that A + B is diagonal c) If A. B are diagonal, show that AB = BA

Problem 25. A square matrix is a diagonal if aij = 0 whenever i j. a) If A is diagonal, prove that A is diagonal, in fact, how is AT related to A b) If A, B are diagonal, prove that A + B is diagonal c) If A. B are diagonal, show that AB = BA

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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Problem 25. A square matrix is a diagonal if aij = 0 whenever i j. a) If A is diagonal, prove that A™ is diagonal, in fact, how is AT related to A? b) If A, B are diagonal, prove that A + B is diagonal c) If A, B are diagonal, show that AB BA -=
Transcribed Image Text:Problem 25. A square matrix is a diagonal if aij = 0 whenever i j. a) If A is diagonal, prove that A™ is diagonal, in fact, how is AT related to A? b) If A, B are diagonal, prove that A + B is diagonal c) If A, B are diagonal, show that AB BA -=
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