Question 2: Consider the following two statements: Statement 1: If V …

Consider the following two statements:

Statement 1: If $V$ is defined as follows:

$V = \{(x,y) \mid x,y \in \mathbb{R}, x + y = 0\}$

Addition: $(x_1, y_1) + (x_2, y_2) = (x_1 + x_2, y_1 + y_2)$; $(x_1, y_1), (x_2, y_2) \in V$

Scalar multiplication: $c(x, y) = (x, cy)$; $(x, y) \in V$, $c \in \mathbb{R}$

Then $V$ is a vector space.

Statement 2:

If $W = Span\{(1,0,1), (0,1,1), (2,-1,1), (2,-2,-1)\}$, then $dim(W) = 3$.

Which of the following options is true?