DeterminantHard
Question
The determinant 
= 0, If
= 0, IfOptions
A.x, y, z are in AP
B.x, y, z are in GP
C.x, y, z are in HP
D.xy, yz, zx are in AP
Solution
Given, = 0
Applying C1 → C1 - (pC2 + C3)
⇒
⇒ - (xp2 + yp + yp + z) (xz + y2) = 0
∴ Either xp2 + 2yp + z = 0 or y2 = 0
⇒ x, y, z are in GP.
= 0 Applying C1 → C1 - (pC2 + C3)
⇒
⇒ - (xp2 + yp + yp + z) (xz + y2) = 0
∴ Either xp2 + 2yp + z = 0 or y2 = 0
⇒ x, y, z are in GP.
Create a free account to view solution
View Solution FreeMore Determinant Questions
If B is a non-singular matrix and A is a square matrix, then det (B-1 AB) is equal to...Let a determinant is given by A = and suppose determinant A = 6. If B = then -...For any ᐃABC, the value of determinant is -...If the system of equations x + 2y + 3z = 4, x + py + 2z = 3, x + 4y + μz = 3 has an infinite number of solutions, t...The value of the determinant is equal to -...