Question 9: What is the dimension of W2?\ Note: Enter your answer to …

Consider the vector space $\mathbb{R}^3$ with usual addition and scalar multiplication. Let $S$ be its subset defined as follows:

$S = \{(1,-1,0), (0,1,1)\}$

and $W_1$ and $W_2$ be its vector subspaces defined as:

$W_1 = \{(x,y,z) \mid y = z - x; x,y,z \in \mathbb{R}\}$

$W_2 = \{(x,y,z) \mid x = z, \text{ and } y = z; x,y,z \in \mathbb{R}\}$

Answer the given subquestions.

What is the dimension of W2?
Note: Enter your answer to the nearest integer.