Problem 1
1.1 If A is an n x n matrix, prove that if A has n linearlyindependent eigenvalues, then AT is diagonalizable.
1.2 Diagonalize the matrix below with eigenvalues equal to -1and 5.
1.3 Assume that A is 4 x 4 and has three different eigenvalues,if one of the eigenspaces is dimension 1 while the other isdimension 2, can A be undiagonalizable? Explain.
Answer for all 3 questions required.
