Please provide hint on this proof | Mathematics | Page 1

meager gateBOT Jan 26, 2023, 8:25 AM

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martin(ping-me-when-reply)

brisk dagger Jan 26, 2023, 8:25 AM

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I am not sure how to prove this.

magic mirage Jan 26, 2023, 8:26 AM

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Well, find (A^T)^(-1), then (A^(-1))^T.

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You will see that they are equal.

brisk dagger Jan 26, 2023, 8:26 AM

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But that is not a general proof?

magic mirage Jan 26, 2023, 8:27 AM

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Why? It is.

brisk dagger Jan 26, 2023, 8:27 AM

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But isn't that for a specific example?

magic mirage Jan 26, 2023, 8:27 AM

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No.

brisk dagger Jan 26, 2023, 8:27 AM

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How do I write an inverse with arbitrary terms?

magic mirage Jan 26, 2023, 8:27 AM

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You can pick A in general form.

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Well, do you remember how to generally find the inverse?

brisk dagger Jan 26, 2023, 8:28 AM

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It actually hasn't been taught in this book.

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We are meant to prove this without knowing that.

magic mirage Jan 26, 2023, 8:28 AM

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Oh... Huh.

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That's a bit odd... Alright, let me think of another way.

brisk dagger Jan 26, 2023, 8:28 AM

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Maybe that's why I'm confused. As of right now Matrix inverses are not very formalized to me, so I didn't realize there was a general way.

magic mirage Jan 26, 2023, 8:32 AM

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Alright, have you learned the property (AB)^T = B^T A^T?

brisk dagger Jan 26, 2023, 8:33 AM

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Yes thank you that's all I needed

brisk dagger Jan 26, 2023, 8:33 AM

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magic mirage Alright, have you learned the property (AB)^T = B^T A^T?

Thanks

lean burrowBOT Jan 26, 2023, 8:33 AM

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@brisk dagger has given 1 rep to @magic mirage

#Please provide hint on this proof