JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
Let \(A=\begin{bmatrix} 1 & 2 & 7 \\ 4 & -2 & 8 \\ 3 & 8 & -7 \end{bmatrix}\) and \(\det(A-\alpha I)=0\), where \(\alpha\) is a real number. If the largest possible value of \(\alpha\) is \(p\), then the circle \((x-p)^2+(y-2p)^2=320\), intersects the co-ordinate axes at
- A \(1\) point
- B \(2\) points
- C \(3\) points
- D \(4\) points
Answer & Solution
Correct Answer
(C) \(3\) points
Step-by-step Solution
Detailed explanation
The characteristic equation is given by \(\det(A-\alpha I) = 0\). \(\det \begin{bmatrix} 1-\alpha & 2 & 7 \\ 4 & -2-\alpha & 8 \\ 3 & 8 & -7-\alpha \end{bmatrix} = 0\) Expanding the determinant along the first row:…
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