A matrix M is symmetric if M = Mt and skew-symmetric (or antisymmetric) if M = -Mt. Assume that the dimensions of each matrix allow the stated operations. Mark each statement as True or False. ✓ A¹A = AAt A. True ✓ det(A¹) = det(A) B. False ✓ (AB)t = BtAt (AA)t = AAt ✓ If AB = BA, then AtBt = Bat ✓ If A is an n x n matrix, then A + A¹ is symmetric ✓ If A is an n x n matrix, then A - At is symmetric If A is symmetric, then A is not skew-symmetric

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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A matrix M is symmetric if M = Mt and skew-symmetric (or antisymmetric) if M = -Mt.
Assume that the dimensions of each matrix allow the stated operations. Mark each statement as True or False.
✓ A¹A = AAt
A. True
✓ det(A¹) = det(A)
B. False
✓ (AB)t = BtAt
(AA)t = AAt
✓ If AB = BA, then AtBt = Bat
✓ If A is an n x n matrix, then A + A¹ is symmetric
✓ If A is an n x n matrix, then A - At is symmetric
If A is symmetric, then A is not skew-symmetric
Transcribed Image Text:A matrix M is symmetric if M = Mt and skew-symmetric (or antisymmetric) if M = -Mt. Assume that the dimensions of each matrix allow the stated operations. Mark each statement as True or False. ✓ A¹A = AAt A. True ✓ det(A¹) = det(A) B. False ✓ (AB)t = BtAt (AA)t = AAt ✓ If AB = BA, then AtBt = Bat ✓ If A is an n x n matrix, then A + A¹ is symmetric ✓ If A is an n x n matrix, then A - At is symmetric If A is symmetric, then A is not skew-symmetric
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