Linear Algebra Are the following sets V vector spaces? Prove or give a counter example. (a) V = R^2 and F = R where vector addition and scalar multiplication is defined as: (x_1, y_1) + (x_2, y_2) =...

Linear Algebra

Are the following sets V vector spaces? Prove or give a counter example.
(a) V = R^2 and F = R where vector addition and scalar multiplication is defined as:

(x_1, y_1) + (x_2, y_2) = (x_1 + y_2, y_1 + x_2), c(x_1, y_1) = (cx_1, cy_1).