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Exercise 3.2.19

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It would be $m$ . Since the range of $A$ is a subspace with dimension $m$ in $𝔽^{m}$ , we know that $L_{A} (𝔽^{n}) = 𝔽^{⋗}$ . Similarly we also have that $L_{B} (𝔽^{p}) = 𝔽^{n}$ . So we know that

L_{A} B (𝔽^{p}) = L_{A} (L_{B} (𝔽^{p})) = 𝔽^{m}

and hence the rank of $AB$ is $m$ .

jephianlin

2011-06-27 00:00

Exercise 3.2.19

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