Question:

Let 𝑀 be a 3Γ—3 real matrix. If 𝑃=𝑀+𝑀𝑇 and 𝑄=𝑀-𝑀𝑇, then which of the following statements is/are always TRUE?

Updated On: Oct 13, 2024
  • det(𝑃 2𝑄 3 )=0
  • trace(𝑄+𝑄 2 )=0
  • 𝑋 𝑇𝑄 2𝑋=0, for all π‘‹βˆˆβ„3
  • 𝑋 𝑇𝑃𝑋 = 2𝑋 𝑇𝑀𝑋, for all 𝑋 ∈ ℝ3
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The Correct Option is A, D

Solution and Explanation

The correct options are: A and D
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