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Unformatted text preview: you try it. 2. To clarify problem 13 of Section 9.6: we are considering solutions of n linear equations in n unknowns, that is, the equations have the form A x = b , where A is an n n matrix, x is a column vector of n unknowns, and b is a given vector with n components. Here are the equations written out, but it is much better to work with the matrix/vector notation: a 11 x 1 + a 12 x 2 + + a 1 n x n = b 1 a 21 x 1 + a 22 x 2 + + a 2 n x n = b 2 . . . . . . . . . . . . . . . a n 1 x 1 + a n 2 x 2 + + a nn x n = b n In (a) we assume that b = ; in part (b) b is arbitrary. To say that the set of solutions is a vector space is to say that a linear combination x (1) + x (2) of two solutions x (1) and x (2) is again a solution. 1...
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- Fall '07