### Problem Statement **4.** For the same \( X = [X_1, X_2, X_3] \) where the clusters are \( X_1 = \begin{bmatrix} 0 \\ 2 \end{bmatrix} \), \( X_2 = \begin{bmatrix} 1 \\ 2 \\ 3 \end{bmatrix} \), \( X_3 = \begin{bmatrix} 4 \\ 2 \end{bmatrix} \), find the within-cluster and between-cluster scatter matrices \( S_w \) and \( S_b \).

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