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JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
Suppose \(A\) is any \(3\times3\) non-singular matrix and \((A - 3I) (A- 5I)\, = 0\), where \(I\,= I_3\) and \(O\,= O_3\). If \(\alpha A + \beta A^{- 1}\, = 4I\), then \(\alpha + \beta \) is equal to
- A \(8\)
- B \(12\)
- C \(13\)
- D \(7\)
Answer & Solution
Correct Answer
(A) \(8\)
Step-by-step Solution
Detailed explanation
we have \((A-3I)(A-5I)=0\) \( \Rightarrow {A^2} - 8A + 15I = 0\) Multiplying both sides by \({A^{ - 1}}\), we get; \({A^{ - 1}}A.A - 8{A^{ - 1}}A + 15{A^{ - 1}}I = {A^{ - 1}}0\) \( \Rightarrow A - 8I + 15{A^{ - 1}} = 0\) \(A + 15{A^{ - 1}} = 8I\)…
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