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posted by  thomas j on 3/25/2008 11:25:24 PM  |  status: Live  

Another Linear Algebra proof (Lifesaver)

Course Textbook Chapter Problem
Linear Algebra Elementary Linear Algebra (9th) by Anton 6.6 N/A
Question Details:
Prove that if a Matrix A is orthogonal, then Det(A)=1 or Det(A)= -1.
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posted by RPGillespie on 3/25/2008 11:45:27 PM  |  status: Live
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thomas j's comment:
"thank you"
Response Details:
If Matrix A is orthogonal, then ATA = I

So,
ATA = I
det(ATA) = det(I)
det(AT)det(A) = 1...........∴ det(AT) = det(A)
det(A)det(A) = 1
det(A)2 = 1
det(A) = ±√1
det(A) = ±1
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