8_Matrices - 16 . Show that (A t ) t = A. 17 . Show that...

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9/20/11
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9. Show that A + (B+C) = (A+B) + C, where A, B and C are matrices of order mxn. 11 . If AB and BA are defined, what can you say regarding the sizes of A and B?
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12a . Show that (A + B)C = AC + BC, where A, B and C are matrices and the sum A+B and products AC and BC are defined. Each dij can be rewriten as the sum of the dot produts of row i of A with column j of C and row i of B with column j of C.
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Unformatted text preview: 16 . Show that (A t ) t = A. 17 . Show that (a) (A+B) t = A t +B t and (b) (AB) t = B t A t , where A and B are nxn matrices. 22 . Show that (AA t ) t = AA t , where A is an nxn matrix. 21 . Show that (A n )-1 = (A-1 ) n , where A is a nonsingular nxn matrix. Show that (AB)-1 = B-1 A-1 , where A and B are nonsingular nxn matrices. Properties of inverses Properties of Determinants...
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8_Matrices - 16 . Show that (A t ) t = A. 17 . Show that...

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