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11 Nov 2019
Hello there!
Any assistance with full working is greatly appreciated, thankyou! :)
In this problem we have the symmetric matrix Calculate the characteristic polynomial det(A - lambda I 3). Find the eigenvalues of A. For each eigenvalue of A, find an orthonormal basis for the corresponding eigenspace. Find an orthogonal matrix P and a diagonal matrix D so that PtAP = D. Show that for each real number mu and for each n 1, (A + mu I3)n = P(D + mu I 3)nPt. In particular, calculate (A + I3)3.
Hello there!
Any assistance with full working is greatly appreciated, thankyou! :)
In this problem we have the symmetric matrix Calculate the characteristic polynomial det(A - lambda I 3). Find the eigenvalues of A. For each eigenvalue of A, find an orthonormal basis for the corresponding eigenspace. Find an orthogonal matrix P and a diagonal matrix D so that PtAP = D. Show that for each real number mu and for each n 1, (A + mu I3)n = P(D + mu I 3)nPt. In particular, calculate (A + I3)3.
Deanna HettingerLv2
12 Apr 2019