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Uaing the properties O have Tearnea Symme tric are is matricese (Hint: The se proofs should only be obout3 ste. each 2 man matrix, then AAT ond an

Uaing the properties O have Tearnea Symme tric are is matricese (Hint: The se proofs should only be obout3 ste. each 2 man matrix, then AAT ond an

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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4.) Sammetric Matrices; A square matrix is said to be is symmetric hat matrixd and shou that Tsing the ae saidl to be symmetric if As A, So ito show a matria have 'to take tHhe transpose of the get the have learned matrix, then AAT ond 'A are summetric matricese CHint: The se proofs should only be obout3 steps original matrit bock. that if A frove propertics an man each 2
Transcribed Image Text:4.) Sammetric Matrices; A square matrix is said to be is symmetric hat matrixd and shou that Tsing the ae saidl to be symmetric if As A, So ito show a matria have 'to take tHhe transpose of the get the have learned matrix, then AAT ond 'A are summetric matricese CHint: The se proofs should only be obout3 steps original matrit bock. that if A frove propertics an man each 2
Expert Solution
Step 1

Given A is any m×n matrix.

Claim:  AAT  is symmetric.

Proof: Consider (AAT)T =AAT  Using the property of transpose i.e (AB)T=BTAT and (AT)T=A

Thus AAT  is symmetric.

 

 

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