Word Count : 606

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दी गई मैट्रिक्स है: [ A = \begin{bmatrix} 1 & 1 & 1 \ 1 & 2 & 1 \ 3 & 2 & 3 \end{bmatrix} ] सबसे पहले आइगेन मान (\lambda) निकालने के लिए हम (\det(A - \lambda I) = 0) हल करेंगे। [ A - \lambda I = \begin{bmatrix} 1-\lambda & 1 & 1 \ 1 & 2-\lambda & 1 \ 3 & 2 & 3-\lambda \end{bmatrix} ] डिटर्मिनेंट: [ \det(A - \lambda I) = (1-\lambda)\begin{vmatrix}2-\lambda & 1 \ 2 & 3-\lambda\end{vmatrix} * 1 \begin{vmatrix}1 & 1 \ 3 & 3-\lambda\end{vmatrix} - 1 \begin{vmatrix}1 & 2-\lambda \ 3 & 2\end{vmatrix} ] पहले छोटे 2×2 डिटर्मिनेंट्स निकालें: 1. (\begin{vmatrix}2-\lambda & 1 \ 2 & 3-\lambda\end{vmatrix} = (2-\lambda)(3-\lambda) - (2)(1) = _______ ___ _________ ___ ______ ______ ______ ____ _________.
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