Archive
17th of March 2017
Mathematics
Q:

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

Srishti Saxena - CBSE - Class XII Science

Friday, March 17, 2017 at 17:37:PM

A:

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

Friday, March 17, 2017 at 21:27:PM