GATE XE (Engineering Sciences) 2022 - Question 19

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Section: Engineering Mathematics | Marks: 2

Let 𝐴 and 𝐡 be π‘›ΰ΅ˆπ‘› matrices with real entries. Consider the following statements: P: If 𝐴 is symmetric then π‘Ÿπ‘Žπ‘›π‘˜αˆΊπ΄αˆ»ΰ΅Œ Number of nonzero eigenvalues (counting multiplicity) of 𝐴. Q: If 𝐴𝐡ࡌ𝟎 then π‘Ÿπ‘Žπ‘›π‘˜αˆΊπ΄αˆ»ΰ΅…π‘Ÿπ‘Žπ‘›π‘˜αˆΊπ΅αˆ»ΰ΅‘π‘›. Then

  • A. both P and Q are TRUE
  • B. P is TRUE and Q is FALSE
  • C. P is FALSE and Q is TRUE
  • D. both P and Q are FALSE

Answer: A. both P and Q are TRUE

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