Скачать или смотреть Solve in Seconds: Matrices Class 12 Shortcut for Higher Powers of Special Matrices

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Solve in Seconds: Higher Powers of Special Matrices
Discussed Questions:
Let P =
1 0 0
4 1 0
16 4 1
and I be the identity matrix of order 3. If Q = [qij] is a matrix
such that P50 – Q = I, then 𝑞31+𝑞32/𝑞21equals [JEE (Adv.] 2016 (Paper-2)]
Let A = 1 𝑎 𝑎 0 1 b 0 0 1 𝑎 , 𝑏 ∈ 𝑅. If for some 𝑛 ∈ 𝑁, 𝐴 𝑛 = 1 48 2160 0 1 96 0 0 1 then 𝑛 + 𝑎 + 𝑏 is equal to [JEE Mains 2022]
If 𝑃 = 3 2 1 2 −1 2 3 2 , 𝐴 = 1 1 0 1 and Q = 𝑃𝐴𝑃 𝑇 . If 𝑃 𝑇𝑄 2007𝑃 = 𝑎 𝑏 𝑐 d , then 2𝑎 + 𝑏 − 3𝑐 − 4𝑑 is equal to [JEE Mains 2023]
Let A = 1 2 −2 0 1 and P= cos𝜃 −sin𝜃 sin𝜃 cos𝜃 ,. If B = 𝑃𝐴𝑃 𝑇 , C = 𝑃 𝑇𝐵 10𝑃 and the sum of the diagonal elements of 𝐶 is 𝑚 𝑛 , where gcd 𝑚, 𝑛 = 1,then 𝑚 + 𝑛 is: [JEE Mains 2025]

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