Consider the set V of all ordered pains of real numbers u = (u_1, u_2) with addition defined by (x_1, x_2) + (y_1 y_2) = (x_1 + y_i - 1, x_2 + y_2 -1) and scalar multiplication defined the usual way k(x_1, x_2) = (kz_1 kz_2) (a) Show, by providing a specific example, that the vector space property k(x + y) = kx + ky does not bold (b) Identify the 0-object relative to this addition (c) Identify the negative object u for an arbitrary u = (u_1, u_2) relative to this addition and 0 object.
Show transcribed image textConsider the set V of all ordered pains of real numbers u = (u_1, u_2) with addition defined by (x_1, x_2) + (y_1 y_2) = (x_1 + y_i - 1, x_2 + y_2 -1) and scalar multiplication defined the usual way k(x_1, x_2) = (kz_1 kz_2) (a) Show, by providing a specific example, that the vector space property k(x + y) = kx + ky does not bold (b) Identify the 0-object relative to this addition (c) Identify the negative object u for an arbitrary u = (u_1, u_2) relative to this addition and 0 object.