(a) Let 09 - 09 CT A = which has characteristic polynomial CA(x) = -(x - 2)'(x - 5). (i) From the polynomial CA() alone, what can one say about the geometric multiplicities of the eigenvalues 2 and 5? Be as specific as you can. (ii) Now find a basis for the eigenspace associated to the eigenvalue 2, and hence give the geometric multiplicity of that eigenvalue. (b) Let B = 0 1 where ce R. How many eigenvalues does B have and with what ge- ometric multiplicities? Without knowing c, is it possible to determine whether B is diagonalizable? Explain your answers