Explanation Given: ( − 3 x 3 4 ) 3 Formula Used: Power of a quotient rule : ( x y ) n = x n y n , y ≠ 0 Product of Power Rule ( x y ) n = x n y n Power Rule of Exponents: ( x m ) n = x m n Calculation: We have been given the expression ( − 3 x 3 4 ) 3 . On applying the power of a quotient rule ( x y ) n = x n y n , y ≠ 0 ( − 3 x 3 4 ) 3 = ( − 3 x 3 ) 3 4 3

Elementary Algebra For College Students (10th Edition)

10th Edition

ISBN: 9780134759005

Author: Allen R. Angel, Dennis Runde

Publisher: PEARSON

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Chapter 4.1, Problem 120ES

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Chapter 4.1, Problem 119ES

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Question 3 over a field K. In this question, MË(K) denotes the set of n × n matrices (a) Suppose that A Є Mn(K) is an invertible matrix. Is it always true that A is equivalent to A-¹? Justify your answer. (b) Let B be given by 8 B = 0 7 7 0 -7 7 Working over the field F2 with 2 elements, compute the rank of B as an element of M2(F2). (c) Let 1 C -1 1 [4] [6] and consider C as an element of M3(Q). Determine the minimal polynomial mc(x) and hence, or otherwise, show that C can not be diagonalised. [7] (d) Show that C in (c) considered as an element of M3(R) can be diagonalised. Write down all the eigenvalues. Show your working. [8]

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Chapter 4 Solutions

Elementary Algebra For College Students (10th Edition)

Ch. 4.1 - Prob. 1ES Ch. 4.1 - Prob. 2ES Ch. 4.1 - Prob. 3ES Ch. 4.1 - Prob. 4ES Ch. 4.1 - Prob. 5ES Ch. 4.1 - Prob. 6ES Ch. 4.1 - Prob. 7ES Ch. 4.1 - Prob. 8ES Ch. 4.1 - Prob. 9ES Ch. 4.1 - Prob. 10ES

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To simplify:

The expression.