Question 3 (15 marks, C4) Let $V$ be the set $V=\{(x, 1, z) \mid x, z \in \mathbb{R}\} .$ Define the addition $\oplus$ and scalar multiplication $\odot$ on $V$ by $$ \begin{aligned} (X, 1, z) Toplus\left(x^{\prime}, 1, Z^{\prime} ight) &=\left(X+X^{\prime}, 1, Z+Z^{\prime} ight), & k lodot(X, 1, z) &=(k x, 1, k z), & k \in \mathbb{R} \end{aligned} Determine whether the set $V$ with addition $\oplus$ and scalar multiplication $\odot$ is a vector space. Justify your answers. CS.JG.056 $$