Let L(x, y) = (x - y + 2z, 2x + y - z, x + 2y + z), and (u_1 = (1, 0, 1), u_2 = (0, 2, 2), u_2 = (1, 2, 0)) be a basis of R^3. Find the matrix representation of L with respect to the standard basis (e_1, e_2, e_3). Find the transition matrix S from (u_1, u_2, u_3) to (e_1, e_2, e_3). Find the matrix representation of L with respect to (u_1, u_2, u_3).
Show transcribed image textLet L(x, y) = (x - y + 2z, 2x + y - z, x + 2y + z), and (u_1 = (1, 0, 1), u_2 = (0, 2, 2), u_2 = (1, 2, 0)) be a basis of R^3. Find the matrix representation of L with respect to the standard basis (e_1, e_2, e_3). Find the transition matrix S from (u_1, u_2, u_3) to (e_1, e_2, e_3). Find the matrix representation of L with respect to (u_1, u_2, u_3).