$\newcommand{\ones}{\mathbf 1}$

# Linear equations

Which of the following are linear functions $f:\textbf{R}^2 \to \textbf{R}^2$?

The sum of $x_1$, $x_2$, and $x_3$ is zero, the sum of $x_1$ and $x_2$ is one, and the sum of $x_2$ and $x_3$ is one. These equations can be expressed in matrix form as $Ax=b$, with
1. $A=\begin{bmatrix} 1 & 1 & 1 \\ 1 & 1 & 0 \\ 0 & 1 & 1 \end{bmatrix}$
Correct!
2. $A=\begin{bmatrix} 1 & 1 & 0 \\ 1 & 1 & 1 \\ 1 & 0 & 1 \end{bmatrix}$
Incorrect.