Problem 1. 92x² + ... (a) (b) If A is diagonalizable, that is A = ODO¹. Assume a polynomial f(x) = ao + a₁x + +ax". Then (ƒ(2₂) Prove that f(A) = Q 0 0 0 0 0 f(2₂) 0 ... 0 f( 2 Q¹, where A eigenvalues of A. If f(A) = B, where A and B are both n x n diagonalizable matrices and have identical eigenvectors, then prove that f(ai) = Abi, in which ai and Abi are the eigenvalues of A and B. -7 6 Apply (b) to find the solutions of A that satisfies A² -3A+1= -12 11

Q: IV) T F If A = AT, then the eigenvalues of A are real.

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Q: .Let f(x) = ax +b, and g(x) = cx +d. Find a condition on the constants a, b, c, d such that f◦g=g◦f.

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Q: Problem 1. 92x² + (a) If A is diagonalizable, that is A = ODO¹. Assume a polynomial f(x) = ao + ₁x +…

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