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

Question

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 (A) II only (B) I, II and V only (C) III and IV (D) all of these

Tardigrade Admin · Accepted Answer

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

Q. If the value of the determinant $∣ ∣ x 0 - x - 1 i i 22 2 i ∣ ∣$ vanishes, then the value(s) of $x$ is/are
I. -1 ,
II. 0 ,
III. $i$
IV. $- i$
V. 1

II only

I, II and V only

III and IV

all of these

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

Q. If the value of the determinant ∣∣​x0−x​−1ii​222i​∣∣​ vanishes, then the value(s) of x is/are I. -1 , II. 0 , III. i IV. −i V. 1