2AThe linear transformation is givenƒ: R³ →R³ : (x,y,z) → ƒ (x,y,z) = (az, by, cx), a,b,c=R.Determine the representation matrix A of ƒ in terms of the physical basis of R³ andprove that there exists an orthogonal matrix PEM33(R) such that the matrix P-¹AP isdiagonal if and only if a=c.

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Answered: The linear transformation is given f:…

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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The linear transformation is given f: R³ R³: (x,y,z) →ƒ (x,y,z) = (az, by, cx), a,b,c=R. Determine the representation matrix A off in terms of the physical basis of R³ and prove that there exists an orthogonal matrix P=M33(R) such that the matrix P-¹AP is diagonal if and only if a=c.