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Which of the following statements are TRUE?
P. The eigen values of a symmetric matrix are real
Q. The value of the determinant of an orthogonal matrix can only be +1
R. The transpose of a square matrix A has the same eigen values as those of A
S. The inverse of an ‘n × n’ matrix exists if and only if the rank is less than ‘n’
  • a)
    P and Q only
  • b)
    P and R only
  • c)
    Q and R only
  • d)
    P and S only
Correct answer is option 'B'. Can you explain this answer?
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Which of the following statements are TRUE?P. The eigen values of a sy...
P and R are true
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Which of the following statements are TRUE?P. The eigen values of a sy...
P. The eigen values of a symmetric matrix are real - TRUE
This statement is true. The eigenvalues of a symmetric matrix are always real.

Q. The value of the determinant of an orthogonal matrix can only be 1 - TRUE
This statement is true. The determinant of an orthogonal matrix can only be 1 or -1.

R. The transpose of a square matrix A has the same eigen values as those of A - TRUE
This statement is true. The transpose of a matrix does not change its eigenvalues.

S. The inverse of an orthogonal matrix is also orthogonal - TRUE
This statement is true. The inverse of an orthogonal matrix is also orthogonal.
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Which of the following statements are TRUE?P. The eigen values of a symmetric matrix are realQ. The value of the determinant of an orthogonal matrix can only be +1R. The transpose of a square matrix A has the same eigen values as those of AS. The inverse of an ‘n × n’ matrix exists if and only if the rank is less than ‘n’a)P and Q onlyb)P and R onlyc)Q and R onlyd)P and S onlyCorrect answer is option 'B'. Can you explain this answer?
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Which of the following statements are TRUE?P. The eigen values of a symmetric matrix are realQ. The value of the determinant of an orthogonal matrix can only be +1R. The transpose of a square matrix A has the same eigen values as those of AS. The inverse of an ‘n × n’ matrix exists if and only if the rank is less than ‘n’a)P and Q onlyb)P and R onlyc)Q and R onlyd)P and S onlyCorrect answer is option 'B'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Which of the following statements are TRUE?P. The eigen values of a symmetric matrix are realQ. The value of the determinant of an orthogonal matrix can only be +1R. The transpose of a square matrix A has the same eigen values as those of AS. The inverse of an ‘n × n’ matrix exists if and only if the rank is less than ‘n’a)P and Q onlyb)P and R onlyc)Q and R onlyd)P and S onlyCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which of the following statements are TRUE?P. The eigen values of a symmetric matrix are realQ. The value of the determinant of an orthogonal matrix can only be +1R. The transpose of a square matrix A has the same eigen values as those of AS. The inverse of an ‘n × n’ matrix exists if and only if the rank is less than ‘n’a)P and Q onlyb)P and R onlyc)Q and R onlyd)P and S onlyCorrect answer is option 'B'. Can you explain this answer?.
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