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 α x (1) + β x (2) of two solutions x (1) and x (2) is again a solution. 1...
View Full Document
This note was uploaded on 09/29/2009 for the course 642 527 taught by Professor Speer during the Fall '07 term at Rutgers.
- Fall '07