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Math / Discrete Mathematics and Its Applications 7 / Chapter 2.6 / Problem 17E

Discrete Mathematics and Its Applications | 7th Edition | ISBN: 9780073383095 | Authors: Kenneth Rosen

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Let A and B be two n × n matrices. Show thata) (A + B)t =

Chapter 2, Problem 17E

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QUESTION:

Let A and B be two n × n matrices. Show thata) (A + B)t = At +Bt.________________b) (AB) t = B t A t.If A and B arc n × n matrices with AB = BA = In, then B is called the inverse of A (this terminology is appropriate because such a matrix B is unique) and A is said to be invertible. The notation B = A-1 denotes that B is the inverse of A.

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QUESTION:

Let A and B be two n × n matrices. Show thata) (A + B)t = At +Bt.________________b) (AB) t = B t A t.If A and B arc n × n matrices with AB = BA = In, then B is called the inverse of A (this terminology is appropriate because such a matrix B is unique) and A is said to be invertible. The notation B = A-1 denotes that B is the inverse of A.

ANSWER:

Solution:Step 1:According to the question, we have to show that (A + B)T= AT+BT.

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