Explanation Given information: The matrix A is [ 1 − 2 0 3 ] . The matrix B is [ − 3 1 2 − 1 ] Calculation: Find the matrix ( A + B ) as shown below: Substitute [ 1 − 2 0 3 ] for A and [ − 3 1 2 − 1 ] for B . ( A + B ) = [ 1 − 2 0 3 ] + [ − 3 1 2 − 1 ] = [ 1 − 3 − 2 + 1 0 + 2 3 − 1 ] = [ − 2 − 1 2 2 ] Find the matrix ( A − B ) as shown below: ( A − B ) = [ 1 − 2 0 3 ] − [ − 3 1 2 − 1 ] = [ 1 − ( − 3 ) − 2 − 1 0 − ( 2 ) 3 − ( − 1 ) ] = [ 4 − 3 − 2 4 ] Find the matrix ( A + B ) ( A − B ) as shown below: ( A + B ) ( A − B ) = [ − 2 − 1 2 2 ] [ 4 − 3 − 2 4 ] = [ − 2 ( 4 ) + ( − 1 ) ( − 2 ) − 2 ( − 3 ) + ( − 1 ) ( 4 ) 2 ( 4 ) + 2 ( − 2 ) 2 ( − 3 ) + 2 ( 4 ) ] = [ − 8 + 2 6 − 4 8 − 4 − 6 + 8 ] = [ − 6 2 4 2 ] Find the matrix ( A 2 ) as shown below: Substitute [ 1 − 2 0 3 ] for A

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ISBN: 9780134437705

Author: Washington

Publisher: PEARSON

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Chapter 16, Problem 77RE

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Show that (A+B)(A−B)≠A2−B2 by using matrices A and B.

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Chapter 16, Problem 76RE

Chapter 16, Problem 78RE

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Chapter 16 Solutions

Basic Technical Mathematics

Ch. 16.1 - For matrices A and B, find A + B. Ch. 16.1 - Prob. 2PE Ch. 16.1 - Prob. 3PE Ch. 16.1 - Prob. 1E Ch. 16.1 - Prob. 2E Ch. 16.1 - Prob. 3E Ch. 16.1 - Prob. 4E Ch. 16.1 - In Exercises 3–10, determine the value of the...Ch. 16.1 - Prob. 6E Ch. 16.1 - Prob. 7E

Ch. 16.1 - Prob. 8E Ch. 16.1 - In Exercises 3–10, determine the value of the...Ch. 16.1 - Prob. 10E Ch. 16.1 - Prob. 11E Ch. 16.1 - Prob. 12E Ch. 16.1 - Prob. 13E Ch. 16.1 - Prob. 14E Ch. 16.1 - Prob. 15E Ch. 16.1 - Prob. 16E Ch. 16.1 - Prob. 17E Ch. 16.1 - Prob. 18E Ch. 16.1 - Prob. 19E Ch. 16.1 - Prob. 20E Ch. 16.1 - Prob. 21E Ch. 16.1 - Prob. 22E Ch. 16.1 - Prob. 23E Ch. 16.1 - Prob. 24E Ch. 16.1 - Prob. 25E Ch. 16.1 - Prob. 26E Ch. 16.1 - Prob. 27E Ch. 16.1 - Prob. 28E Ch. 16.1 - Prob. 29E Ch. 16.1 - Prob. 30E Ch. 16.1 - Prob. 31E Ch. 16.1 - Prob. 32E Ch. 16.1 - Prob. 33E Ch. 16.1 - Prob. 34E Ch. 16.1 - Prob. 35E Ch. 16.1 - Prob. 36E Ch. 16.1 - Prob. 37E Ch. 16.1 - Prob. 38E Ch. 16.1 - Prob. 39E Ch. 16.1 - Prob. 40E Ch. 16.1 - Prob. 41E Ch. 16.1 - Prob. 42E Ch. 16.1 - Prob. 43E Ch. 16.1 - Prob. 44E Ch. 16.2 - Prob. 1PE Ch. 16.2 - Prob. 2PE Ch. 16.2 - Prob. 3PE Ch. 16.2 - Prob. 1E Ch. 16.2 - Prob. 2E Ch. 16.2 - Prob. 3E Ch. 16.2 - Prob. 4E Ch. 16.2 - Prob. 5E Ch. 16.2 - Prob. 6E Ch. 16.2 - 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Show that ( A + B ) ( A − B ) ≠ A 2 − B 2 by using matrices A and B .

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Show that (A+B)(A−B)≠A2−B2 by using matrices A and B.

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Chapter 16 Solutions