Name ________________________                  Linear Algebra, Quiz 3, Summer 2004  

Problem 1.  Do a complete eigenvalue, eigenvector analysis of the matrix A, including finding the matrix P that diagonalizes A and using P to diagonalize A.

A = matrix([[3, 1, 0], [4, 0, 0], [1, -3, 3]])

 

 

 

 

 

 

 

 

Problem 2.  Find a matrix A that has the following eigenvalues and corresponding eigenvectors. Make sure to show all your work and explain your reasoning.

lambda[1] = 0, lambda[2] = 1, lambda[3] = -1, v[1] = matrix([[0], [1], [-1]]), v[2] = matrix([[1], [-1], [1]]), v[3] = matrix([[0], [1], [1]])