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Engineering Maths · Q68

Linear Algebra

Engineering and GATE · Engineering Maths · question 68

Q68

Consider the matrix \[ P = [ array*20c 1 2 &0& 1 2 \\ 0&1&0 \\ - 1 2 &0& 1 2 array ]\] Which one of the following statements about P is INCORRECT?

Consider the matrix {\text{P}} = \left[ {\begin{array}{*{20}{c}} {\frac{1}{{\sqrt 2 }}}&0&{\frac{1}{{\sqrt 2 }}} \\ 0&1&0 \\ {\frac{{ - 1}}{{\sqrt 2 }}}&0&{\frac{1}{{\sqrt 2 }}} \end{array}} \right]
Which one of the following statements about P is INCORRECT?
A.
Determinant of P is equal to 1
B.
P is orthogonal
C.
Inverse of P is equal to its transpose
D.
All eigen values of P are real numbers
Answer

Answer: Option D

Solution

Answer: Option D
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