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F10MT1 - M341 Fall 2010 First Midterm September 17th 2 3 8...

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M341, Fall 2010, . First Midterm, September 17 th . I. A = ( 2 3 4 6 ) , B = ( 8 4 5 5 ) , C = ( 5 2 3 1 ) . Compute A ( B C ). A ( B C ) = ( 2 3 4 6 ) ( 3 6 2 4 ) = ( 0 0 0 0 ) II. Either perform the following operations or clearly explain why you cannot. 1) A = 1 6 2 5 3 4 , B = 3 5 2 4 1 5 . A + B , A + B T , B + A T , B T + A T . AB , BA , A T B , AB T , BA T , B T A This question was correct in the papers of a large majority of students. However only a few noticed that B T + A T = ( A + B ) T , BA T = ( AB T ) T , and B T A = ( A T B ) T . Since the other operations were not possible because the dimension did not match, in fact there was only 1 addition of matrices and two products. A + B = 2 1 0 1 2 1 , A T + B T = ( A + B ) T = ( 2 0 2 1 1 1 ) A T B = ( 1 2 3 6 5 4 ) = ( 10 28 32 70 ) , B T A = ( A T B ) T = ( 10 32 28 70 ) AB T = ( 33 26 31 31 24 23 ) , BA T = ( AB T ) T = 33 31 29 26 24 22 31 27 23 2) D = ( 2 0 1 4 5 2 ) , E = ( 7 5 1 1 4 3 ) , F = 1 2 2 1 6 5 . 5 E 4 F T , DE , DF , FD , DF FD 5 E 4 F T = ( 31 17 19 3 24 35 ) , It is not possible to multiply D (2 × 3) and E (2 × 3) since the number of columns of D does not match the number of rows of E.
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