Question

If a, b, c, d, e and f are in G.P. then the value of

$\left| \mspace{6mu}\begin{matrix} a^{2} & d^{2} & x \\ b^{2} & e^{2} & y \\ c^{2} & f^{2} & z \end{matrix}\mspace{6mu} \right|$depends on –

• A. x and y
• B. x and z
• C. y and z
• D. Independent of x, y, and z

Answer 1

Answer: (D)

Independent of x, y, and z

Answer 2

b = ar, c = ar², d = ar³, e = ar⁴, f = ar⁵

determinant = $\left| \begin{matrix} a^{2} & a^{2}r^{6} & x \\ a^{2}r^{2} & a^{2}r^{8} & y \\ a^{2}r^{4} & a^{2}r^{10} & z \end{matrix} \right|$= a²a²r⁶$\left| \begin{matrix} 1 & 1 & x \\ r^{2} & r^{2} & y \\ r^{4} & r^{4} & z \end{matrix} \right|$ = 0