University of Wisconsin-Madison Mathematics Department

Math 340 Elementary Matrix and Linear Algebra Lecturer: Arun Ram

Fall 2007

Homework 11: Due November 21, 2007

1. Do problems 2, 4, 6, 10, 24, 26 on page 297.
   
   
2. Do problems 4, 19, 30 on page 318.
   
   
3. Let ⟨,⟩ be the standard inner product on R². Find the matrix of ⟨,⟩ with respect to the basis S given in problem 15 on page 267.
   
   
4. Let ⟨,⟩ be the standard inner product on R². Find the matrix of ⟨,⟩ with respect to the basis T given in problem 15 on page 267.
   
   
5. Let ⟨,⟩ be the standard inner product on R³. Find the matrix of ⟨,⟩ with respect to the basis S given in problem 16 on page 268.
   
   
6. Let ⟨,⟩ be the standard inner product on R³. Find the matrix of ⟨,⟩ with respect to the basis T given in problem 16 on page 268.
   
   
7. Let ⟨,⟩ be the standard inner product on R₃. Find the matrix of ⟨,⟩ with respect to the basis S given in problem 18 on page 268.
   
   
8. Let ⟨,⟩ be the standard inner product on R₃. Find the matrix of ⟨,⟩ with respect to the basis T given in problem 18 on page 268.
   
   
9. Do problem 13 on page 462. Also determine the projections onto the eigenvectors, in terms of the matrix A.
   
   
10. Do problem 18 on page 462. Also determine the projections onto the eigenvectors, in terms of the matrix A.
    
    
11. Do problem 19 on page 462. Also determine the projections onto the eigenvectors, in terms of the matrix A.