Let A Rx3 and suppose that 3 = (v, U2, U3) is an ordered basis...

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Let A € R³x3 and suppose that 3 = (v₁, U2, U3) is an ordered basis for R³ consisting of eigenvectors for A. So Av₁ = A1v₁, Av2 = 22, and Av3 = A3V3 for some scalars A₁, A2, A3 € R. (a) The above equations can be written concisely using matrix notation as AQ = QA. What are the entries of Q and A? What special property does A have? (b) We can multiply both sides of the above equation on the right by Q-¹ to obtain A = QAQ-¹. This factorization of A makes it easy to perform many calculations involving A. What is A2? What is A100? Let A € R³x3 and suppose that 3 = (v₁, U2, U3) is an ordered basis for R³ consisting of eigenvectors for A. So Av₁ = A1v₁, Av2 = 22, and Av3 = A3V3 for some scalars A₁, A2, A3 € R. (a) The above equations can be written concisely using matrix notation as AQ = QA. What are the entries of Q and A? What special property does A have? (b) We can multiply both sides of the above equation on the right by Q-¹ to obtain A = QAQ-¹. This factorization of A makes it easy to perform many calculations involving A. What is A2? What is A100?

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a Entries of Q and and the special property of Matrix Q Q is a 3x3 matrix wh... View the full answer