## Find a Basis and the Dimension of the Subspace of the 4-Dimensional Vector Space

## Problem 131

Let $V$ be the following subspace of the $4$-dimensional vector space $\R^4$.

\[V:=\left\{ \quad\begin{bmatrix}

x_1 \\

x_2 \\

x_3 \\

x_4

\end{bmatrix} \in \R^4

\quad \middle| \quad

x_1-x_2+x_3-x_4=0 \quad\right\}.\]
Find a basis of the subspace $V$ and its dimension.