QUESTION I Consider the operator R³ → R³ given by left-multiplication by the matrix: -6 -8 A = 2 -1 4 -1 6 Find the characteristic polynomial CA(x), the eigenvalues of A, and the eigenspaces of A. What are the algebraic and geometric multiplicities of each eigenvalue? Is A diagonaliz- able?

QUESTION I Consider the operator R³ → R³ given by left-multiplication by the matrix: -6 -8 A = 2 -1 4 -1 6 Find the characteristic polynomial CA(x), the eigenvalues of A, and the eigenspaces of A. What are the algebraic and geometric multiplicities of each eigenvalue? Is A diagonaliz- able?

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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Question

Find the characteristic polynomial cA(x), the eigenvalues of A, and the eigenspaces of A.

What are the algebraic and geometric multiplicities of each eigenvalue? Is A diagonalizable?

QUESTION I
Consider the operator R³ → R³ given by left-multiplication by the matrix:
-6
-8
A =
2
-1
4 -1 6
Find the characteristic polynomial CA(x), the eigenvalues of A, and the eigenspaces of A.
What are the algebraic and geometric multiplicities of each eigenvalue? Is A diagonaliz-
able?

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