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Unformatted text preview: SOLUTION (a) It is easiest to start with the column of BA . By V.I.F. 3 , which is the denition of matrixmatrix multiplication, (column j of BA ) = B (column j of A ) . Since (column j of A ) = e i if j = i if j 6 = i , (column j of BA ) = B e i if j = i if j 6 = i , Since B e j is the j th column of B , we have (column j of BA ) = (column j of B ) and all other columns of BA are zero . This tells us what the columns of BA are. To see what the rows of AB are, note that ( AB ) t = B t A t and A t = A . Thus, ( AB ) t = B t A . 21 /september/ 2005; 22:09 38...
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- Fall '08