2 math questions about Linear Algebra, topics about eigenvalue and eigenvector
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1. Let T : R3 R3 be the linear transformation rotating every vector by 90 degreescounterclockwise around the z-axis. Find the determinant of the associated matrix orexplain why this is impossible. If you give an example (or counterexample), you mustshow why it satisfies the conditions of the problem.
2. . Let A be a 3 3 matrix with eigenvalues 1, 2, 3 and associated eigenvectors e1, e2, e3.Find the eigenvalues and eigenvectors of A1 or explain why this is impossible. If yougive an example (or counterexample), you must show why it satisfies the conditions ofthe problem
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