Write the value of a + i b c + i d - c + i d a - i b .

Given: a + i b c + i d - c + i d a - i b The determinant of the matrix A = a b c d is A = a d - b c . = a + i b a - i b - c + i d - c + i d = a 2 - i a b + i a b - i 2 b 2 - ( - c 2 - i c d + i c d + i 2 d 2 ) = a 2 - i 2 b 2 + c 2 - i 2 d 2 = a 2 + b 2 + c 2 + d 2 ∵ i 2 = - 1 ⇒ a + i b c + i d - c + i d a - i b = a 2 + b 2 + c 2 + d 2 Thus, the determinant value is a 2 + b 2 + c 2 + d 2 .

Write the value of a + i b c + i d - c + i d a - i b .

Given: a + i b c + i d - c + i d a - i b The determinant of the matrix A = a b c d is A = a d - b c . = a + i b a - i b - c + i d - c + i d = a 2 - i a b + i a b - i 2 b 2 - ( - c 2 - i c d + i c d + i 2 d 2 ) = a 2 - i 2 b 2 + c 2 - i 2 d 2 = a 2 + b 2 + c 2 + d 2 ∵ i 2 = - 1 ⇒ a + i b c + i d - c + i d a - i b = a 2 + b 2 + c 2 + d 2 Thus, the determinant value is a 2 + b 2 + c 2 + d 2 .

Find the value of x from the following: x 4 2 2 x = 0

Given that x 4 2 2 x = 0 We know that, the determinant of the matrix A = a b c d is A = a b c d = a d - b c . ⇒ 2 x 2 - 8 = 0 ⇒ 2 x 2 = 8 ⇒ x 2 = 8 2 = 4 ⇒ x = 4 = ± 2 Thus, the value of determinant is ± 2 .