(a) [2 marks] Given that T : R3 > R3 is a linear transformation such that 1 1 0 2 0 2 T0=0,T1=1,T0=2 0 0 o 0 1 2 Write down the standard matrix A of T. Briey explain how you nd A. (b) [2 marks] Without solving characteristic. polynomial, nd all the eigenval ues of the standard matrix A in part (a). (c) [4 marks] Find a basis for each of the eigenspaees of A associated with all the eigenvalues (without using MATLAB). Show your working. (d) [2 marks] Using MATLAB command (with format rat option) > [P D] =eig(A), you will get a matrix P where the three columns are eigenvectors; and a diagonal matrix D where the three diagonal entries are eigenvalues. The asterisk * denotes a very small number and usually represents 0. (i) Write down the two columns of P that are eigenvectors corresponding to the smaller eigenvalue; and the one column that is an eigenvector corresponding to the larger eigenvalue. (ii) Explain the dierences between (i) and the answers in part (c) above