Guys I have a question. The subject is Linear Algebra.
Take this thing:
$$U = \{(x,y,z,t) \in \mathbb{R^4}: x + y + z + t = 0, −x − y + 2t = 0, x + y − z = 0\}$$
$U$ is a linear subspace of $\mathbb{R^4}$.
What are exactly the equations after the colon? And what's their purpose?