Consider the following system of equations:
\[
\begin{pmatrix}
1 & 3 & 2
2 & 2 & -3
4 & 4 & -6
2 & 5 & 2
\end{pmatrix}
\begin{pmatrix} x y z \end{pmatrix} =
\begin{pmatrix} 1 1 2 1 \end{pmatrix}
\]
The value of \( y^2 + z^2 \) is _______.
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In non-square matrices, always check for linear dependencies first. Recognizing that row 3 was a multiple of row 2 immediately reduced the complexity of the problem.