For any matrix A, AAT and ATA are symmetric matrices. Using Properties of the Transpose, we have which of the following? O (AAT)T = A"(AT) = AAT O (AAT)T = A"(ATT) = AAT O (AAT)T = (AT)TAT = AAT O (AAT)T = (AT T)AT = AAT O (AAT)T = (A2T)AT = AAT %3D %3D We also know which of the following to be true? O (ATA)T = A"(ATT) = ATA O (ATA)T = (AT)TAT = A'A O (ATA)T = AT(AT)T = ATA O (ATA)T = AT(A2T) = ATA O (ATA)T = (AT T)AT = ATA %3D So each of AA and ATA is equal to ---Select-- so both matrices are sym

Algebra and Trigonometry (6th Edition)
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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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Prove the given theorem.
For any matrix A, AAT and ATA are symmetric matrices.
Using Properties of the Transpose, we have which of the following?
O (AAT)T = A"(AT) = AA"
O (AAT)T = AT(ATT) = AAT
O (AAT)T = (AT)TAT = AA"
O (AAT)T = (AT T)AT = AAT
O (AAT)T = (A2TJAT = AAT
%3D
%3D
We also know which of the following to be true?
O (ATA)T = AT(AT T) = ATA
O (ATA)T = (AT)TAT = ATA
O (ATA)T = A"(AT)" = A'A
O (ATA)T = AT(A27) = ATA
O (ATA)T = (AT JAT = ATA
%3D
So each of AA' and A'A is equal to ---Select---
so both matrices are symmetric.
Transcribed Image Text:Prove the given theorem. For any matrix A, AAT and ATA are symmetric matrices. Using Properties of the Transpose, we have which of the following? O (AAT)T = A"(AT) = AA" O (AAT)T = AT(ATT) = AAT O (AAT)T = (AT)TAT = AA" O (AAT)T = (AT T)AT = AAT O (AAT)T = (A2TJAT = AAT %3D %3D We also know which of the following to be true? O (ATA)T = AT(AT T) = ATA O (ATA)T = (AT)TAT = ATA O (ATA)T = A"(AT)" = A'A O (ATA)T = AT(A27) = ATA O (ATA)T = (AT JAT = ATA %3D So each of AA' and A'A is equal to ---Select--- so both matrices are symmetric.
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