MATH 1B03 Lecture Notes - Lecture 17: Eigenvalues And Eigenvectors, Diagonalizable Matrix

b) i) Show that the characteristic equation of the 3 x 3 matrix 4 -1 1 B-0 30 1 -1 2 is given by-13 + 9λ2-271 + 27-0, where A is an eigenvalue ii) Show that B has exactly one eigenvalue, and compute the iii) Let c be a scalar. Suppose that A is a matrix similar to cI, show iv) Using your answers to(ii) and (ii), deduce that the matrix B is v) Compute the geometric multiplicity of the eigenvalue of B. of B algebraic multiplicity of this eigenvalue. that A cI not diagonalisable.