JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
Let \(P\) be a square matrix such that \(P ^2= I - P\). For \(\alpha, \beta, \gamma, \delta \in N\), if \(P ^\alpha+ P ^\beta=\gamma I -29 P\) and \(P ^\alpha- P ^\beta=\) \(\delta I-13 P\), then \(\alpha+\beta+\gamma-\delta\) is equal to \(........\).
- A \(18\)
- B \(40\)
- C \(24\)
- D \(22\)
Answer & Solution
Correct Answer
(C) \(24\)
Step-by-step Solution
Detailed explanation
\(P ^2= I - P\) \(P ^\alpha+ P ^\beta=\gamma I -29 P , P ^\alpha- P ^\beta=\delta I -13 P\) \(P ^4=( I - P )^2= I -2 P + P ^2=2 I -3 P\) \(P ^6=(2 I -3 P )( I - P )=5 I -8 P\) \(P ^8=(2 I -3 P )^2=4 I -12 P +9( I - P )=13 I -21 P\) \(P ^8+ P ^6=18 I -29 P\)…
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