The value of the determinant $|\begin{matrix} {(a_{1} - b_{1})}^{2} & {(a_{1} - b_{2})}^{2} & {(a_{1} - b_{3})}^{2} & {(a_{1} - b_{4})}^{2} \\ {(a_{2} - b_{1})}^{2} & {(a_{2} - b_{2})}^{2} & {(a_{2} - b_{3})}^{2} & {(a_{2} - b_{4})}^{2} \\ {(a_{3} - b_{1})}^{2} & {(a_{3} - b_{2})}^{2} & {(a_{3} - b_{3})}^{2} & {(a_{3} - b_{4})}^{2} \\ {(a_{4} - b_{1})}^{2} & {(a_{4} - b_{2})}^{2} & {(a_{4} - b_{3})}^{2} & {(a_{4} - b_{4})}^{2} \end{matrix}|$ is

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

dependant on a_i, i = 1, 2, 3, 4

dependant on b_i, i = 1, 2, 3, 4

dependant on a_ij, b_i, i = 1, 2, 3, 4

answer is D.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

The given determinant, on simplification, gives

$\begin{matrix} Δ_{1} = |\begin{matrix} a_{1}^{2} & - 2 a_{1} & 1 & 0 \\ a_{2}^{2} & - 2 a_{2} & 1 & 0 \\ a_{3}^{2} & - 2 a_{3} & 1 & 0 \\ a_{4}^{2} & - 2 a_{4} & 1 & 0 \end{matrix}| \times |\begin{array}{cccc} 1 & b_{1} & b_{1}^{2} & 0 \\ 1 & b_{2} & b_{2}^{2} & 0 \\ 1 & b_{3} & b_{3}^{2} & 0 \\ 1 & b_{4} & b_{4}^{2} & 0 \end{array}| \\ = 0 \times 0 = 0 \end{matrix}$