CUET · MATHS · PYQ PAPER 2023
If \(A=\left(\begin{array}{cc}1 & 0 \\ -1 & 7\end{array}\right), I=\left(\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right)\), and \(A^2=8 A+K I\) the value of \(K\) is :
- A 7
- B \(-7\)
- C 8
- D \(-8\)
Answer & Solution
Correct Answer
(B) \(-7\)
Step-by-step Solution
Detailed explanation
\(\text{tr}(A) = 1+7 = 8\) \(\det(A) = (1)(7)-(0)(-1) = 7\) \(A^2 - \text{tr}(A)A + \det(A)I = 0 \Rightarrow A^2 = 8A - 7I\) \(8A - 7I = 8A + KI\) \(K = -7\)
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