1. Tardigrade
  2. Question
  3. Mathematics
  4. If the value of the determinant | x -1 2 0 i 2 - x i 2 i| vanishes, then the value(s) of x is/are I. -1 , II. 0 , III. i IV. - i V. 1

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Q. If the value of the determinant $\begin{vmatrix} x & -1 & 2 \\ 0 & i & 2 \\ - x & i & 2 i\end{vmatrix}$ vanishes, then the value(s) of $x$ is/are
I. -1 ,
II. 0 ,
III. $i$
IV. $- i$
V. 1

Determinants

Solution:

$D = x (- 2 - 2i) - x (- 2 - 2i) = - 2x (1 + i) + 2x (1 + i) =$ zero
Hence, D vanishes for all values of x.