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समान्यत: आइगेनवैल्यू और आइगेनवेक्टर ज्ञात करने के लिए हमें पहले आव्यूह (matrix) का चरित्र समीकरण (characteristic equation) निकालना होता है। दी गई आव्यूह है: \[ B = \begin{bmatrix} 1 & 1 & 0 \\ -1 & 3 & 0 \\ 1 & -1 & 1 \end{bmatrix} \] ### 1. चरित्र समीकरण का निर्धारण: हमारा लक्ष्य है \( B \) का डिटरमिनेंट \( |B - \lambda I| = 0 \), जहाँ \( \lambda \) आइगेनवैल्यू है और \( I \) पहचान मैट्रिक्स (identity matrix) है। पहले \( B - \lambda I \) की गणना करते हैं: \[ B - \lambda I = \begin{bmatrix} 1 - \lambda & 1 & 0 \\ -1 & 3 - \lambda & 0 __________ ____ _____ ________ _______ _________ __________ ________ ________ _________ ________ _______.
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