CUET · MATHS · PYQ PAPER 2023
Given \(X=\left[\begin{array}{cc}1 & 0 \\ -1 & 7\end{array}\right]\), then value of K if \(X^2=8 X+K I\) is :
- A \(-7\)
- B 7
- C 8
- D 5
Answer & Solution
Correct Answer
(A) \(-7\)
Step-by-step Solution
Detailed explanation
\(\det(X - \lambda I) = \det\left(\begin{bmatrix} 1-\lambda & 0 \\ -1 & 7-\lambda \end{bmatrix}\right) = (1-\lambda)(7-\lambda) = \lambda^2 - 8\lambda + 7\) Characteristic equation: \(\lambda^2 - 8\lambda + 7 = 0\) By Cayley-Hamilton theorem:…
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