Solve these questions please

Question 3 (10 marks) a) Given that set B = {(1, 2, -1) , (-1, -1,2), (1, -1, -3) } is a basis of R3. i. What is the transition matrix which will change bases from B to the standard basis of R3? (1 mark) ii. What is the transition matrix that will change bases from the standard basis of R3 to B. (4 marks) iii. Use one of the transition matrices that you calculated above (you need to pick the correct one) to calculate the coordinate vector of (1, 0, -1) relative to basis B. (2 marks b) A linear transformation f : R3 - R3 is defined by the formula f (1, 202, 23) = (21 - 272 +23, 421 +22+ 213, 221+262+23). i. Write down the standard matrix of f, i.e. the matrix with respect to the standard basis of R3 (1 mark) ii. Show that f is a one-to-one transformation. (2 marks) Question 4 (10 marks) Let T be a linear transformation from 3 to R2 defined by T ( x, y, z) = (2x+ y+ z,x-y-z) (2) a) Find the matrix of T with respect to the bases B1 = {(1, -1, 1) , (1, 2, -3), (-2, 1, -1) } and B2 = {(1, -2) , (1, -1) }. (5 marks) b) Use the matrix found in part a) to find T(v), where (v) B, = (2, 1, 1) hence v = (1, 1, -2) . Compare this with the result you obtain by using formula (2).