Let p(A) = A(X – 1)2(A – 2)*(A – 4)5 be the characteristic polynomial of a %3D matrix A. (a) Find all of the eigenvalues of A, along with their algebraic multiplicities. Use what you've found to compute the order of A. (b) Suppose that the nullspace of A is a three-dimensional. Compute the rank of A. Is A diagonalizable? Explain.

Let p(A) = A(X – 1)2(A – 2)*(A – 4)5 be the characteristic polynomial of a %3D matrix A. (a) Find all of the eigenvalues of A, along with their algebraic multiplicities. Use what you've found to compute the order of A. (b) Suppose that the nullspace of A is a three-dimensional. Compute the rank of A. Is A diagonalizable? Explain.

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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