Texts:
(1) Determine whether the transformation is linear.
(a) T : R2 → R2, where T ((x1, x2)) = (√3x1 − 1, 5x2, 4x2).
(b) T : R2 → R2, where T ((x1, x2)) = (x1 + 2, 7x1 + 8x2).
(2) Suppose T : R2 → R2 is a linear transformation and there is a basis B = {→u1, →u2} such that T (→u1) = (2, 3), and T (→u2) = (-5, 7). If [-→v]B = (a, b), then find T (→v).