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Study the data carefully and answer the questions given below:
For any square matrix P, defined matrices Q = P + PT, R = P − PT, then:
  • a)
    Both Q and R are anti-symmetric
  • b)
    R is anti-symmetric and Q is symmetric
  • c)
    Both are symmetric
  • d)
    None of the above is true
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
Study the data carefully and answer the questions given below:For any...
If A is symmetric then AT = A and if is anti-symmetric then AT = −A
We can start with finding the transpose of given expressions like,
⇒ (P + PT)T = PT + P and
⇒ (P − PT)T = PT − P
⇒ (P − PT)T = −(P − PT)
Hence we can say that,
Q = P + PT and R = P − PT are symmetric and anti-symmetric respectively.
Hence, the correct option is (B).
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Study the data carefully and answer the questions given below:For any square matrix P, defined matrices Q = P + PT, R = P − PT, then:a)Both Q and R are anti-symmetricb)R is anti-symmetric and Q is symmetricc)Both are symmetricd)None of the above is trueCorrect answer is option 'B'. Can you explain this answer?
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