Word Count : 654

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To find the minimal polynomial of the given matrix \[ A = \begin{bmatrix}2 & 1 & 0 & 1 \\ -1 & 0 & 0 & 1 \\ -2 & -2 & -1 & 3 \\ 0 & 0 & 0 & 1\end{bmatrix} \] we proceed with the following steps: ### Step 1: Compute the Characteristic Polynomial The characteristic polynomial is given by: \[ \chi_A(\lambda) = \det(A - \lambda I) \] \[ A - \lambda I = \begin{bmatrix} 2 - \lambda & 1 & 0 & 1 \\ -1 & -\lambda & 0 & 1 \\ -2 & -2 & -1 - \lambda & 3 \\ 0 & 0 _________ ______ _____ _______ _____ ____.
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