GATE XE (Engineering Sciences) 2024 - Question 19

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Section: Engineering Mathematics | Type: MSQ | Marks: 2

Let 𝑃 and 𝑄 be two square matrices of the same order. Then, which of the following matrices is/are necessarily equal to (𝑃+ 2𝑄)2 ?

  • A. 𝑃2 + 4𝑃𝑄+ 4𝑄2
  • B. 𝑃(𝑃+ 2𝑄) + 𝑄(2𝑃+ 4𝑄)
  • C. (𝑃+ 2𝑄)(2𝑄+ 𝑃)
  • D. 𝑃2 + 2𝑃𝑄+ 2𝑄𝑃+ 4𝑄2

Answer: B. 𝑃(𝑃+ 2𝑄) + 𝑄(2𝑃+ 4𝑄); C. (𝑃+ 2𝑄)(2𝑄+ 𝑃); D. 𝑃2 + 2𝑃𝑄+ 2𝑄𝑃+ 4𝑄2

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