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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.

Advanced Engineering Mathematics
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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8. Diagonalisation Consider the matrix A = 9 -6 -12 8 -13 -24 -2 6 11 i. Determine the characteristic equation D(A) 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. iv. Construct P from the eigenvectors, then find P-1 (either using Gauss-Jordan elimination or the cofactors method) and then check P-¹AP to verify the correctness of your solutions.
Transcribed Image Text:8. Diagonalisation Consider the matrix A = 9 -6 -12 8 -13 -24 -2 6 11 i. Determine the characteristic equation D(A) 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. iv. Construct P from the eigenvectors, then find P-1 (either using Gauss-Jordan elimination or the cofactors method) and then check P-¹AP to verify the correctness of your solutions.
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