Suppose $R^2 = \{ [y_1 y_2]^T | y_1, y_2 \in R \}$ where $[y_1 y_2]^T \oplus [z_1 z_2]^T = [y_1 + z_2, y_2 + z_1]^T$ and $c \odot [y_1 y_2]^T = [cy_1 cy_2]^T$. \newline Identify what properties of vector space $(2+8)$ are not satisfied or satisfied by $(R^2, \oplus, \odot)$. Then, show if $(R^2, \oplus, \odot)$ is a vector space.