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Home » \Rightarrow x^2 - 2x + 1 + y^2 + z^2 - 2z + 1 = 2 - Crosslake

\Rightarrow x^2 - 2x + 1 + y^2 + z^2 - 2z + 1 = 2 - Crosslake

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 \[ \det(A - \lambda I) = 0 \]

📌 For matrix \( A = egin{bmatrix} 4 & 1 \ 2 & 3 \end{bmatrix} \), the characteristic equation is:

📌 \[ \det egin{bmatrix} 4 - \lambda & 1 \ 2 & 3 - \lambda \end{bmatrix} = 0 \]

📌 \[ (4 - \lambda)(3 - \lambda) - 2 \cdot 1 = 0 \]

📌 \[ (4 - \lambda)(3 - \lambda) - 2 = 0 \]

📌 \[ (12 - 4\lambda - 3\lambda + \lambda^2) - 2 = 0 \]

📌 \[ \lambda^2 - 7\lambda + 10 = 0 \]

📌 \[ \lambda = rac{7 \pm \sqrt{(-7)^2 - 4 \cdot 1 \cdot 10}}{2 \cdot 1} \]

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