8. Diagonalisation Consider the matrix A= 9 -6 -12] -13 -24 11 -2 ܚܪ ܝ 6 i. Determine the characteristic equation D(X) for A. ii. Show that D(-1) = 0 and use this information to factorise the characteristic equation using polynomial division and find the remaining eigenvalues. Comment on whether or not we can tell if A is diagonalisable at this stage. iii. Find the corresponding eigenvectors.

8. Diagonalisation Consider the matrix A= 9 -6 -12] -13 -24 11 -2 ܚܪ ܝ 6 i. Determine the characteristic equation D(X) for A. ii. Show that D(-1) = 0 and use this information to factorise the characteristic equation using polynomial division and find the remaining eigenvalues. Comment on whether or not we can tell if A is diagonalisable at this stage. iii. Find the corresponding eigenvectors.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.4: Similarity And Diagonalization

Problem 6EQ

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