|(A')"| = |S¯¹ ||A"||S|, where we haveused |AB| = |A||B|.(A')n = S-¹A¹S(A')n = [S¹ AS][S¯¹ AS] ... [S¹ AS]where the terms in square brackets arerepeated n times.|(A')"| = |S¯¹S||A", where we haveused |AB| = |A||B|. Therefore |(A')"| = |S¯¹ A"S||(A')"| = |S¹||S||A"|.|(A')"| = |I||A", where I is the identitymatrix.Hence |(A')"| = |A"|, as |I| = 1 for anyidentity matrix.(A')¹ = S-¹ AA ... AS, where the Amatrices are repeated n times.

Problem is to rearrange the given logic.

Answered: Therefore | (A')"| = |S¯¹ A"S| |(A')"|…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Therefore | (A')"| = |S¯¹ A"S| |(A')"| = |S¯¹ ||S||A"|. |(A')"| = |I||A", where I is the identity matrix. Hence |(A')"| = |A"|, as |I| = 1 for any identity matrix. (A')n = S-¹AA... AS, where the A matrices are repeated n times.