Word Count : 459

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To verify the Cayley-Hamilton theorem for the matrix \( A = \begin{bmatrix} 1 & -1 \\ 0 & 2 \end{bmatrix} \), we will follow these steps: 1. Find the characteristic polynomial of the matrix. 2. Substitute the matrix \( A \) into its characteristic polynomial. 3. Verify if the result is the zero matrix. ### Step 1: Find the characteristic polynomial The characteristic polynomial \( p_A(\lambda) \) is given by the determinant of \( A - \lambda I \), where \( I \) is the identity matrix and \( \lambda \) ___ ___ _________ ___ ____ ________ ________ _____ ___ _______ _______ ________.
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