$\mathbf{V} = \{(a, b) : a, b \in\mathbb{R}\}$
$\mathbf{F} = \mathbb{R}$(Real)
Addition: $ x = (x_1, y_1), y = (x_2, y_2), x + y = (x_1 + x_2, y_1 + y_2)$
Scalar multiplication: $ x = (x_1, y_1), \alpha x = (\alpha x_1, \alpha y_1)$
$\mathbf{V}$ is a Vector space
$$
$\mathbf{F} = \mathbb{R}$(Real)
Addition: $ x = (x_1, y_1), y = (x_2, y_2), x + y = (x_1 + x_2, y_1 + y_2)$
Scalar multiplication: $ x = (x_1, y_1), \alpha x = (\alpha x_1, \alpha y_1)$
$\mathbf{V}$ is a Vector space
$$
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