# 2.9 - Section 2.9 Transposes Definition The transpose of A...

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Section 2.9 Transposes Definition : The transpose of A, denoted A T , is found by interchanging the rows and columns of A. Example : Let 123 456 A  =   find A T . 14 25 36 T A = Note that if A is mXn then A T is nXm.

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Properties (Theorem): If A & B are mXn matrices and C is nXm, then (a) (A + B) T = A T + B T (b) (AC) T = C T A T Note that here AC is mXm. Since C T is mXn and A T is nXm, then C T A T is mXm. A T C T would be nXn, the "wrong" size. (c) (A T ) T = A (d) If A is square, then det(A) = det (A T ) (e) If A is square and invertible, then (A -1 ) T = (A T ) -1 Example : Find (A T )
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## This note was uploaded on 10/16/2009 for the course MATH 1114 at Virginia Tech.

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2.9 - Section 2.9 Transposes Definition The transpose of A...

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