Let R2.2 denote the vector space of real 22 matrices, and consider its standard basis C = (E11, E12, E21, E22), where " E-(0) E12= ( ). E21 = = ( %). E22= =(89). Let f be the endomorphism of R2.2 defined by = (1)-(4%). (1)-(4%). 1 (6) - (433). 1 (60) - (22). -3 (a) Decide whether it is true or false that the matrix M(f) associated to f with respect to the standard ba is giving reasons for your answer. (b) Compute a basis of Ker(). 2 2 0 0 0 0 0 0 D= -2 -1 -1 0 2 1 1 0 (c) Compute a basis of Im(f). (d) Find all eigenvalues of f together with their algebraic and geometric multiplicities. (e) Decide, giving reasons for your answers, whether or not D is diagonalizable. 1,700 x 1,126