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Exercise 3.3.10

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The answer is Yes. Say the matrix is $A$ . Since the matrix has rank $m$ , we have that dimension of $R (L_{A})$ is $m$ . But this means $R (L_{A}) = 𝔽^{m}$ since the codomain of $L_{A}$ is $𝔽^{m}$ and it has dimension $m$ . So it must has a solution by the previous exercise.

jephianlin

2011-06-27 00:00

Exercise 3.3.10

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