Question: Nonlinear functions. Show that the following two functions \(f: \mathbf{R}^{3} \rightarrow \mathbf{R}\) are not linear.

1. \(f(x)=\left(x_{1}-x_{2}+x_{3}\right)^{2}\).
2. \(f(x)=\left(x_{1}+2 x_{2}-x_{3}\right)_{+}\) where for any real number \(a,(a)_{+}\) is the positive part of \(a\), defined as \((a)_{+}=\max (a, 0) .\)

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