-14 6 20 -1 0 02 2 16 0 2Let A =so that Aa(t) = (t + 1)²(t – 2)². Define T : R' → R“ byT(x) = Ax.(a) For each eigenvalue A, find a basis B, for the generalized eigenspace K, by firstfinding a basis for Ex = N(A- AI) and extending to a basis for K = N(A-AI)².(b) Let B = B-1U B2. Find the matrix [T|B of T relative to the basis B and find amatrix P such that P-AP = [T\B. Recall that A = [T]E, where E is the standard basis, hence P isa matrix such that P-'[T]pP= [T]B.

We have to find a basis for the generalized eigenspace and we can proceed further.

-1 4 6 2 0 -1 0 0 Let A = so that A4(t) = (t+ 1)²(t – 2)². Define T : Rª → Rª by 2 2 1 6 0 2 T(x) = Ax. (a) For each eigenvalue A, find a basis B, for the generalized eigenspace K, by first finding a basis for E, = N(A– AI) and extending to a basis for KA = N(A–AI)². (b) Let B = B_1 U B2. Find the matrix [T]B of T relative to the basis B and find a matrix P such that P-'AP = [T]B.

-1 4 6 2 0 -1 0 0 Let A = so that A4(t) = (t+ 1)²(t – 2)². Define T : Rª → Rª by 2 2 1 6 0 2 T(x) = Ax. (a) For each eigenvalue A, find a basis B, for the generalized eigenspace K, by first finding a basis for E, = N(A– AI) and extending to a basis for KA = N(A–AI)². (b) Let B = B_1 U B2. Find the matrix [T]B of T relative to the basis B and find a matrix P such that P-'AP = [T]B.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter7: Eigenvalues And Eigenvectors

Section7.CR: Review Exercises

Problem 64CR: a Find a symmetric matrix B such that B2=A for A=[2112] b Generalize the result of part a by proving...

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