Prove Lemma 4.5. Let B be an n n matrix and let E be an n
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Prove Lemma 4.5.
Let B be an n × n matrix and let E be an n × n elementary matrix. Then
det(EB) = (det E) (det B)
We can use Lemma 4.5 to prove the main theorem of this section: a characterization of invertibility in terms of determinants.
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We will apply Theorems 43 and 44 to prove Lemma 45 detEB det Edet B We consider each type of ele...View the full answer
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