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Prove Theorem Let A, B and C be m x n matrices m and let s and t .pdf

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Prove Theorem: Let A, B and C be m x n matrices m and let s and t be anyscalars. Than: A + B = B + A Let A, B and C be m x n matrices m and let s and t be anyscalars. Than: A + B = B + A Solution Let A= (aij)mxn and B=(bij)mxn A+B =(aij)mxn +(bij)mxn = (aij+bij)mxn =(bij+aij)mxn = ( bij)mxn+( aij)mxn =B+A =B+A.

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Prove Theorem: Let A, B and C be m x n matrices m and let s and t be anyscalars. Than: A + B = B + A Let A, B and C be m x n matrices m and let s and t be anyscalars. Than: A + B = B + A Solution Let A= (aij)mxn and B=(bij)mxn A+B =(aij)mxn +(bij)mxn = (aij+bij)mxn =(bij+aij)mxn = ( bij)mxn+( aij)mxn =B+A =B+A

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  • 1. Prove Theorem: Let A, B and C be m x n matrices m and let s and t be anyscalars. Than: A + B = B + A Let A, B and C be m x n matrices m and let s and t be anyscalars. Than: A + B = B + A Solution Let A= (aij)mxn and B=(bij)mxn A+B =(aij)mxn +(bij)mxn = (aij+bij)mxn =(bij+aij)mxn = ( bij)mxn+( aij)mxn =B+A =B+A