Hi can someone help with this question, thank you. 1. (a) Suppose that X is a 3×3 diagonalizable matrix and that {u1,u2,u3}  is a basis of R3  consisting of eigenvectors of X  with corresponding eigenvalues λ1,λ2,λ3. Suppose that the matrix Y is also a 3×3 diagonalizable matrix with the same eigenvectors as X, although with possibly different eigenvalues ℓ1,ℓ2,ℓ3. Prove that 2X−3Y  is diagonalizable.   (b) Suppose that two square matrices A  and B both have their characteristic polynomial equal to p(λ)=−λ3+4λ. Prove that A is similar to B.

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