Question 10, Exercise 2.1

Solutions of Question 10 of Exercise 2.1 of Unit 02: Matrices and Determinants. This is unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB) Peshawar, Pakistan.

Question 10

Let A=[1−34−32−54−50] and B=[5676−83731]. Verify that A and B are symmetric. Also verify that A+B is symmetric.

Solution

A=[1−34−32−54−50] B=[5676−83731] For symmetric, we have to find out, A=At B=Bt (A+B)t=At+Bt At=[1−34−32−54−50] Bt=[5676−83731] A=[1−34−32−54−50] A=At B=[5676−83731] B=Bt A+B=[1−34−32−54−50]+[5676−83731] A+B=[1+5−3+64+7−3+62−8−5+34+7−5+30+1] A+B=[63113−6−211−21] (A+B)t=[63113−6−211−21] At+Bt=[1−34−32−54−50]+[5676−83731] At+Bt=[1+5−3+64+7−3+62−8−5+34+7−5+30+1] At+Bt=[63113−6−211−21] (A+B)t=At+Bt

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