Question: Please write clearly, thank you very much Let AMnn(F). Prove the following statements. (a) If {v1,,vn} is a basis for Fn that triangularizes LA, then

Please write clearly, thank you very much Let AMnn(F). Prove the

Please write clearly, thank you very much

Let AMnn(F). Prove the following statements. (a) If {v1,,vn} is a basis for Fn that triangularizes LA, then the matrix Q=(v1vn)Mnn(F) is invertible, and Q1AQ is upper triangular. (b) Conversely, if QMnn(F) is an invertible matrix such that Q1AQ is upper triangular, then the column vectors of Q form a basis for Fn that triangularizes LA

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