Homework 2

Math 414 Homework 2, Spring 2007

          Professor Sachs

          due: Wednesday, Feb. 7

          Problems from text:

          Section 4.1: 4.1.2, 4.1.8, 4.1.9 (do after the one below)

         Also solve:

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          For a real symmetric matrix A show all eigenvalues have a full
          set of eigenvectors by showing that after shifting the eigenvalue
          to 0 by using A- lambda I=B, if B^2 x = 0 then Bx=0. Hint: take
          dot product of x with B^2 x, use symmetry.

          Then conclude that if B^n x=0 it follows that Bx=0 by induction.

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          Find the Fourier series for the periodic extension of |x| on the interval
          [-pi, pi]