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Exercise 3.2.21

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Let $β = {e_{1}, e_{2}, \dots, e_{m}}$ be the standard basis for $𝔽^{m}$ . Since the rank of $A$ is $m$ , we know that $L_{A}$ is surjective. So we can find some vector $v_{i} \in 𝔽^{n}$ such that $L_{A} (v_{i}) = e_{i}$ . So let $B$ be the matrix with column vector $v_{i}$ . Thus $B$ is an $n \times m$ matrix and $AB = I$ since $A v_{i} = e_{i}$ .

jephianlin

2011-06-27 00:00

Exercise 3.2.21

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