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To find the characteristic roots (eigenvalues) and characteristic vectors (eigenvectors) of the matrix \( A \), we need to follow these steps: Given the matrix: \[ A = \begin{bmatrix} 4 & 4 \\ 1 & 0 \end{bmatrix} \] ### Step 1: Find the characteristic equation The characteristic equation is given by: \[ \det(A - \lambda I) = 0 \] where \( \lambda \) is the eigenvalue, and \( I \) is the identity matrix. So, \[ A - \lambda I = \begin{bmatrix} 4 & 4 \\ 1 & 0 \end{bmatrix} ______ _____ ___ ________ _____.
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