1. Consider the following set 1 D 1 1 U 1 8 0' 1' 1 1 1 1 0 l 1 (a) [2 marks] Is the set 3 an orthogonal basis for 1114? (b) [4 marks] Convert the set S into an orthonormal basis for 111*. Leave your answers in surds if necessary. 2. Let 1 a 1 1 1 2 1 0 0 a A' 2 a 2 U wdb' a 2 1 0 2 a [a] [3 marks] Find a basis for the column space of A. {b} [5 marks] Find all the least square solution to Ax = b. [e] [2 marks] Find the projection of 13 onto the eelumn spaee of A. 3. Let T : 1R3 > R3 be the linear transformation I zy+z T a = a .3 231; (a) [2 marks] Find the standard matrix of the linear transformation T. (b) [2 marks] Find the eigenvalues of the standard matrix of T