Linear Algebra 63.a.Transpose Matrices Operations, proof

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I'm not sure these proof are right. Because some time you use proof to solve the proof. Its not a justification of property. If I wrong please correct me.

pcspictures
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many thanks. Am new to this so am still trying to clear up what we "can" and "can't" do in a proof.

Triplechoco
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You're saving me here, Thanks a mil !!!

chemist
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Really needed this. Thank you so much!

kevindao
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Thanks a lot!! Bookmark 3:36 proof of ABt BtAt

rbrgkpi
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While multiplying 2 matrix the order of column of first matrix and row of second matrix must be equal Herre they are different

justsimple
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[is there any other way to prove number 4 by the whole matrix i mean A, B and not by its elements i mean a[i, j

osrihai
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Sir how you did (aikbkj)^T equals to ajkbki

NabeelMustafaSMM