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For any sqare matrix A prove that A+A' is a symmetric matrix

Asked by neesa.vs 17th March 2017, 5:37 PM
Answered by Expert
Answer:

begin mathsize 16px style Let space us space assume space matrix space straight A equals open square brackets table row straight a straight b row straight c straight d end table close square brackets
Then space straight A apostrophe space is space transpose space of space matrix space straight A space as space straight A apostrophe equals open square brackets table row straight a straight c row straight b straight d end table close square brackets space space

Now comma
straight A plus straight A apostrophe equals open square brackets table row cell 2 straight a end cell cell straight b plus straight c end cell row cell straight c plus straight b end cell cell 2 straight d end cell end table close square brackets equals open square brackets table row cell 2 straight a end cell cell straight b plus straight c end cell row cell straight b plus straight c end cell cell 2 straight d end cell end table close square brackets
Take space transpose space of space straight A plus straight A apostrophe space comma
open parentheses straight A plus straight A apostrophe space close parentheses apostrophe equals open square brackets table row cell 2 straight a end cell cell straight b plus straight c end cell row cell straight b plus straight c end cell cell 2 straight d end cell end table close square brackets space equals space straight A plus straight A apostrophe space
Hence space proved.


end style

Answered by Expert 17th March 2017, 9:27 PM
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