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CBSE Class 12-science Answered

For any sqare matrix A prove that A+A' is a symmetric matrix
Asked by neesa.vs | 17 Mar, 2017, 05:37: PM
answered-by-expert 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 | 17 Mar, 2017, 09:27: PM

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