I could really use some step-by-step help on these two problems please. Thank You in advance.
1.) Let $V = \{{\bf{A|A}}$ is an $n \times n$ matrix, $n$ fixed, det$({\bf{A}}) = 0$ }. Is $V$, with the usual addition and
scalar multiplication, a vector space? Give reason. If yes, find the dimension and a basis for $V$.
2.) Let $V = \{f(x)|f(x) = (ax + b)e^{-x},\; a,b\; \in\; \mathbb{R}\}$. Is $V$, with the usual addition and scalar
multiplication, a vector space? Give reason. If yes, find the dimension and basis for $V$.