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Consider the similarity transform of a matrix a to A’ given A’ = S-1AS. You need to prove | A n | = ( A’ ) n . Arrange the statements in the correct order so as to obtain to complete proof of this result. See image attached

Consider the similarity transform of a matrix a to A’ given A’ = S-1AS. You need to prove | A n | = ( A’ ) n . Arrange the statements in the correct order so as to obtain to complete proof of this result. See image attached

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Consider the similarity transform of a matrix a to A’ given A’ = S-1AS. You need to prove | A n | = ( A’ ) n . Arrange the statements in the correct order so as to obtain to complete proof of this result. See image attached

Therefore |(A')"| = |S¯¹ A"S| |(A')"| = |S¹||S||A"|. |(A')"| = |I||A", where I is the identity matrix. Hence |(A')"| = |A"|, as |I| = 1 for any identity matrix. (A')¹ = S-¹ AA ... AS, where the A matrices are repeated n times.
Transcribed Image Text:Therefore |(A')"| = |S¯¹ A"S| |(A')"| = |S¹||S||A"|. |(A')"| = |I||A", where I is the identity matrix. Hence |(A')"| = |A"|, as |I| = 1 for any identity matrix. (A')¹ = S-¹ AA ... AS, where the A matrices are repeated n times.
|(A')"| = |S¯¹ ||A"||S|, where we have used |AB| = |A||B|. (A')n = S-¹A¹S (A')n = [S¹ AS][S¯¹ AS] ... [S¹ AS] where the terms in square brackets are repeated n times. |(A')"| = |S¯¹S||A", where we have used |AB| = |A||B|.
Transcribed Image Text:|(A')"| = |S¯¹ ||A"||S|, where we have used |AB| = |A||B|. (A')n = S-¹A¹S (A')n = [S¹ AS][S¯¹ AS] ... [S¹ AS] where the terms in square brackets are repeated n times. |(A')"| = |S¯¹S||A", where we have used |AB| = |A||B|.
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