Which of the transformations in Exercise 1 of Section 8.3 are onto?
Exercise 1 of Section 8.3
In each part, find ker(T), and determine whether the linear transformation T is one-to-one.
(a) T: R2 → R2, where T(x, y) = (y, x)
(b) T: R2 → R2, where T(x, y) = (0, 2x + 3y)
(c) T: R2 → R2, where T(x, y) = (x + y, x - y)
(d) T: R2 → R3, where T(x, y) = (x, y, x + y)
(e) T: R2 → R3, where T(x, y) = (x - y, y - x, 2x - 2y)
(f) T: R3 → R2, where T(x, y, z) = (x + y + z, x - y - z)