8. Diagonalisation Consider the matrix A: = 9 -6 - 12 8 -13 -24 -2 6...

 

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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(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. 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. 5 marks 8. Diagonalisation Consider the matrix A: = 9 -6 - 12 8 -13 -24 -2 6 11 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. 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. 5 marks 8. Diagonalisation Consider the matrix A: = 9 -6 - 12 8 -13 -24 -2 6 11 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. 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. 5 marks 8. Diagonalisation Consider the matrix A: = 9 -6 - 12 8 -13 -24 -2 6 11 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. 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. 5 marks 8. Diagonalisation Consider the matrix A: = 9 -6 - 12 8 -13 -24 -2 6 11 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. 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. 5 marks 8. Diagonalisation Consider the matrix A: = 9 -6 - 12 8 -13 -24 -2 6 11 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. 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. 5 marks 8. Diagonalisation Consider the matrix A: = 9 -6 - 12 8 -13 -24 -2 6 11 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. 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. 5 marks 8. Diagonalisation Consider the matrix A: = 9 -6 - 12 8 -13 -24 -2 6 11 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. 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. 5 marks

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A i DA det AXI 9 8 2 det 13 6 9 91 8 2 12 24 11 13... View the full answer