Problem 1: Define L : R3 R? to be the linear transformation with L(m,y,z) = ($+2:9':3323,$+y+z)_ 1 2 0 S is the standard basis for R while B = 20, =3, -4 is another basis for R3. 2 5 -3 (a) [1 mark] Determine the standard matrix of the linear transformation [L]. (b) [1 mark] Write down the change of coordinates matrix Ps. p from B-coordinates to S- coordinates. (Hint: This is easy.) () [2 marks] Find the change of coordinates matrix Pg. s from S-coordinates to B-coordinates. (d) [2 marks] Compute the matrix product Pg.s[L|Ps . Instructor's Comment: this matrix takes a vector in B-coordinates, converts to the standard basis, applies the transformation L, then converts back to B-coordinates