Test 1, On Ch. 7-9. March 30, 1998

1. Find the spectral radius for the matrix
   

   1  0  0
   2  2  0
   3  1 -1
   

2. Apply two steps of the Gauss-Seidel method with the zero initial guess to the system Ax=b with
   

        1  0  0             1
   A =  0 -1  0    and  b = 0
        0  1 -1             0  
   

3. Compute the linear least-squares polynomial for the following data
   

   x = 0 1 2
   y = 1 0 1
   

4. Find orthogonal polynomials of the degree zero, one, and two on the interval [-1,0].