Unformatted text preview: A . Thus, (column 2 of B t A t ) = 1 1 1 1 + 3 2 2 + 1 1 + 2 3 2 1 . ( ** ) But the columns of B t are the rows of A , so by ( * ), the right hand side of ( ** ) expresses second row of AB as a linear combination of the rows of B . 5.5 Let A be a 3 × 3 matrix whose column representation is A = [ v 1 , v 2 , v 3 ]. Find an explicit numerical 3 × 3 matrix B so that AB = [ v 2 + v 3 , v 1 + v 2 , v 1 + v 2 ] . (You are looking for a single B that works no matter what v 1 , v 2 and v 3 happen to be. SOLUTION The given information expresses the ﬁrst column of AB as a linear combination of the columns of A , namely v 2 + v 3 . By the second part of Theorem 13, the ﬁrst 21 /september/ 2005; 22:09 37...
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 Fall '08
 Gladue
 Calculus, Linear Algebra, Vector Space, Dot Product, Linear combination

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