Question: Linear functions. For each description of \(y\) below, express it as \(y=A x\) for some \(A\). (You should specify \(A\).)

1. \(y_{i}\) is the difference between \(x_{i}\) and the average of \(x_{1}, \ldots, x_{i-1} .\left(\right.\) We take \(\left.y_{1}=x_{1} .\right)\)
2. \(y_{i}\) is the difference between \(x_{i}\) and the average value of all other \(x_{j} \mathrm{~s}\), i.e., the average of \(x_{1}, \ldots, x_{i-1}, x_{i+1}, \ldots, x_{n}\).

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