1. Find the eigenvalues and corresponding eigenvectors of T: R² → R² where the transformation is given by T(x1, x2) = (2x, - X2, -X1 + 2xz). i. Also, find the trace and determinant of the matrix A =...

1. Find the eigenvalues and corresponding eigenvectors of T: R? -> I? where the
transformation is given by T(r,*2) = (2x, - *2, -* + 2x2).
i.Also, find he aseand determinant of the malts A =13 7)
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.

Extracted text: 1. Find the eigenvalues and corresponding eigenvectors of T: R² → R² where the transformation is given by T(x1, x2) = (2x, - X2, -X1 + 2xz). i. Also, find the trace and determinant of the matrix A = ii. What are the eigenvalues of A² and A-1 ? ii. Determine whether A is diagonalizable. If it is, identify an invertible matrix P, such that A is diagonalizable and find P-'AP.