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1. Find the eigenvalues and corresponding eigenvectors of T: R² R? where the transformation is given by T(x1,x2) = (2x1 – x2, –x1 + 2x2). 2 Also, find the trace and determinant of the matrix A =| , i. ii. What are the eigenvalues of A? and A¬1 ? iii. Determine whether A is diagonalizable. If it is, identify an invertible matrix P, such that A is diagonalizable and find P¬'AP.

1. Find the eigenvalues and corresponding eigenvectors of T: R² R? where the transformation is given by T(x1,x2) = (2x1 – x2, –x1 + 2x2). 2 Also, find the trace and determinant of the matrix A =| , i. ii. What are the eigenvalues of A? and A¬1 ? iii. Determine whether A is diagonalizable. If it is, identify an invertible matrix P, such that A is diagonalizable and find P¬'AP.

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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1. Find the eigenvalues and corresponding eigenvectors of T: R? → R² where the transformation is given by T(x1,x2) = (2x1 – x2, –x1 + 2x2). 2 Also, find the trace and determinant of the matrix A =| i. ii. What are the eigenvalues of A² and A¬1 ? iii. Determine whether A is diagonalizable. If it is, identify an invertible matrix P, such that A is diagonalizable and find P¬1AP.
Transcribed Image Text:1. Find the eigenvalues and corresponding eigenvectors of T: R? → R² where the transformation is given by T(x1,x2) = (2x1 – x2, –x1 + 2x2). 2 Also, find the trace and determinant of the matrix A =| i. ii. What are the eigenvalues of A² and A¬1 ? iii. Determine whether A is diagonalizable. If it is, identify an invertible matrix P, such that A is diagonalizable and find P¬1AP.
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