jee-main 2023 Q76

jee-main · India · session2_06apr_shift2 Matrices Matrix Power Computation and Application

Let $P$ be a square matrix such that $P^{2} = I - P$. For $\alpha, \beta, \gamma, \delta \in \mathbb{N}$, if $P^{\alpha} + P^{\beta} = \gamma I - 29P$ and $P^{\alpha} - P^{\beta} = \delta I - 13P$, then $\alpha + \beta + \gamma - \delta$ is equal to
(1) 18
(2) 40
(3) 22
(4) 24

Let $P$ be a square matrix such that $P^{2} = I - P$. For $\alpha, \beta, \gamma, \delta \in \mathbb{N}$, if $P^{\alpha} + P^{\beta} = \gamma I - 29P$ and $P^{\alpha} - P^{\beta} = \delta I - 13P$, then $\alpha + \beta + \gamma - \delta$ is equal to\\
(1) 18\\
(2) 40\\
(3) 22\\
(4) 24

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