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Unformatted text preview: A x = b , where A = 1 2 11 1 1 1 and b = 1 1 1 1 .. (Use the normal equation.) 4 9. (20 pts) Find the eigenvalues and eigenvectors of the matrix ± 233 2 ² . Then ﬁnd a matrix P so that P1 AP = ± 51 ² . 10. (15 pts) Answer the following questions. Be concise, but give the whole answer. • If A is m × n, rank( A ) = n, and A x = b has a solution, then the solution is unique. Why? • If A x = b is inconsistent, then we can get a least squares approximate solution by solving A x = b r . How is b r obtained from b ? • If A is a square matrix and can be row reduced to the identity, then ( A  I ) is reduced by the same operations to ( I  B ). How do we know that B = A1 ? 5...
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This note was uploaded on 05/23/2008 for the course MATH 290/291 taught by Professor Lerner during the Spring '08 term at Kansas.
 Spring '08
 LERNER
 Math, Linear Algebra, Algebra

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