Find T(v) by using the matrix relative to B and B'. T: R2 → R3, T(x, y) = (x + y, x, y), v = (7, 4), B = {(1, −1), (0, 1)},B' ={(1, 1, 0),(0, 1, 1),(1, 0, 1)}

Let f(u, v) = (u - v, 1, u + v) and g(x, y, z) = xyz. Find the entry a12 (i.e. the entry in the first row and second column) of the derivative matrices Df(u, v), Dg(x, y, z) and D(gof)(0, 1). (a) a 12 of Df(u, v) is (b) a12 of Dg(x, y, z) is (c) a12 of D(gof)(0, 1) is (d) Select the correct answer about D(g. f)(u, v) D(gof)(u, v) is a 1 x 2 matrix. D(gof)(u, v) is a 2 x 2 matrix. D(gof)(u, v) is a 3 x 2 matrix. D(gof)(u, v) is a 2 x 3 matrix. D(gof)(u, v) is a real-valued function of u and v. (e) Select the correct answer about D(f g)(x, y, z) OD(fog)(x, y, z) is not defined. D(fog)(x, y, z) is a real-valued function of x and y. D(fog)(x, y, z) is a 3 x 2 matrix. D(fog)(x, y, z) is a 2 x 2 matrix. D(fog)(x, y, z) is a 2 x 1 matrix.