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Exercise 10.A.5

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Proof. Suppose $B$ is an $n$ -by- $n$ matrix. Let $V$ denote an $n$ -by- $n$ dimensional vector space and let $v_{1}, \dots, v_{n}$ be a basis of $V$ . Define $T \in L (V)$ such that $M (T, (v_{1}, \dots, v_{n})) = B$ . By 5.27, there is a basis $u_{1}, \dots, u_{n}$ of $V$ such that $M (T, (u_{1}, \dots, u_{n}))$ is upper triangular. The equation written in 10.7 completes the proof. □

celiopassos

2017-10-06 00:00

Exercise 10.A.5

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