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GATE | GATE-CS-2016 (Set 1) | Question 15

  • Last Updated : 06 Oct, 2021

Two eigenvalues of a 3 x 3 real matrix P are (2 + √ -1) and 3. The determinant of P is _____
Note : This question was asked as Numerical Answer Type.
(A) 0
(B) 1
(C) 15
(D) -1

Answer: (C)

Explanation: The determinant of a real matrix can never be imaginary. So, if one eigen value is complex, the other eigen value has to be its conjugate.
So, the eigen values of the matrix will be 2+i, 2-i and 3.
Also, determinant is the product of all eigen values.
So, the required answer is (2+i)*(2-i)*(3) = (4-i2)*(3) = (5)*(3) = 15.
Thus, C is the required answer.

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