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  3. (a) suppose that a is a 3 x 3 diagonalizable matri

(a) Suppose that A is a 3 x 3 diagonalizable matrix with a basis of...

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(a) Suppose that A is a 3 x 3 diagonalizable matrix with a basis of eigenvectors of R given by {u?, U?, U3} with corresponding eigenvalues A1, A2, A3. Suppose that the matrix B is also a 3 x 3 diagonalizable matrix with the same eigenvectors although with possibly different eigenvalues 11, 12, 13. Prove that A + B is also a diagonalizable matrix.(b) Suppose that the square matrices A and B are similar. Prove that the matrices A2+ A+ I and B2 +B+ I are also similar.(c) Suppose that the square matrices A and B both have their characteristic polynomial equal to - + X. Prove that A is similar to B.

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