Question 1 (labs 1,2) Consider the following matrix A = 0 3 0 3 1. Matrix A has one repeated eigenvalue. Give an expression for all possible eigenvectors that corre- spond to the repeated eigenvalue of A. Write your answer in the form 11/2 where a and b are some constants and u; and wi, (i = 1, 2,3, 4) are the smallest possible integers. Explain how you obtained the answer. 2. Using your answer from part (1), determine a relationship between a and b so that |v| = 1. Give your answer in the form f(a, b) = 1, where f(a, b) is a certain combination of a and b. 3. How many different eigenvectors v can you find that correspond to the repeated eigenvalue of A? Justify your answer. 4. Determine if the vector -0.235695189327704 1.178518373045391 U = -0.235702260395516 0.707106781186548 is an eigenvector of A. 5. Is matrix A diagonalizable? Justify your