Explanation Given: The provided matrices are A = [ − 3 − 9 2 6 ] , B = [ 4 6 2 3 ] . Formula used: Let A be an m × n matrix and let B be an n × k matrix. The product matrix A B is the m × k matrix whose entry in the i t h row and j t h column is the product of the i t h row of A and the j t h column of B . Proof: Consider: A + B = [ − 3 − 9 2 6 ] + [ 4 6 2 3 ] = [ − 3 + 4 − 9 + 6 2 + 2 6 + 3 ] = [ 1 − 3 4 9 ] Now, ( A + B ) 2 = [ 1 − 3 4 9 ] [ 1 − 3 4 9 ] = [ ( 1 ) ( 1 ) + ( − 3 ) ( 4 ) ( 1 ) ( − 3 ) + ( − 3 ) ( 9 ) ( 4 ) ( 1 ) + ( 9 ) ( 4 ) ( 4 ) ( − 3 ) + ( 9 ) ( 9 ) ] = [ 1 − 12 − 3 − 27 4 + 36 − 12 + 81 ] Therefore, ( A + B ) 2 = [ − 11 − 30 40 69 ] ... … ( 1 ) Now, consider, A 2 = [ − 3 − 9 2 6 ] [ − 3 − 9 2 6 ] = [ ( − 3 ) ( − 3 ) + ( − 9 ) ( 2 ) ( − 3 ) ( − 9 ) + ( − 9 ) ( 6 ) ( 2 ) ( − 3 ) + ( 6 ) ( 2 ) ( 2 ) ( − 9 ) + ( 6 ) ( 6 ) ] = [ 9 − 18 27 − 54 − 6 + 12 − 18 + 36 ] = [ − 9 "

Mathematics with Applications In the Management, Natural and Social Sciences (11th Edition)

11th Edition

ISBN: 9780321931078

Author: Margaret L. Lial, Thomas W. Hungerford, John P. Holcomb, Bernadette Mullins

Publisher: PEARSON

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Chapter 6.5, Problem 20E

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To prove: The matrices (A+B)2≠A2+2AB+B2.

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Chapter 6.5, Problem 19E

Chapter 6.5, Problem 21E

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Chapter 6 Solutions

Mathematics with Applications In the Management, Natural and Social Sciences (11th Edition)

Ch. 6.1 - Checkpoint1 Use the substitution method tosolve...Ch. 6.1 - Checkpoint 2 Use the elimination method to solve...Ch. 6.1 - Checkpoint 3 Solve the system of equations . Draw...Ch. 6.1 - Checkpoint 4 Solve the following system: Ch. 6.1 - Checkpoint 5 Solve the system Draw the graph of...Ch. 6.1 - Prob. 6CP Ch. 6.1 - Prob. 1E Ch. 6.1 - Prob. 2E Ch. 6.1 - Use substitution to solve each system. (See...Ch. 6.1 - Use substitution to solve each system. (See...

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To prove: The matrices ( A + B ) 2 ≠ A 2 + 2 A B + B 2 .

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To prove: The matrices (A+B)2≠A2+2AB+B2.

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Chapter 6 Solutions