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Unformatted text preview: n . Problem 3. Consider the matrix, A = 3 1-1 1 9 3 5-6-4 . Find a basis for each of the subspaces: R ( A ), R ( A T ) , N ( A ) and N ( A T ) . What is the rank of A ? Problem 4 Calculate the matrix coordinate representation for the linear operator, D ( p ( t )) = dp ( t ) dt-p ( t ) , on the space of polynomials of degree three on the interval [-1,1]. Use Chebyshev polynomials (of the ±rst kind) as the basis for the space. If you are unfamiliar with Chebyshev polynomials you can ±nd a recurrence relation for generating them on Wikipedia. Problem 5. Consider Ax = b and suppose we are given a vector c ∈ R ( A T ) . Show that c T x is constant for all x that are solutions to the normal equations A T Ax = A T b . 1...
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This note was uploaded on 12/10/2009 for the course ECE 210a taught by Professor Roysmith during the Fall '09 term at Santa Barbara City.
- Fall '09