Question

If a, b, c are non zero real numbers then

$\left| \begin{matrix} b^{2}c^{2} & bc & b + c \\ c^{2}a^{2} & ca & c + a \\ a^{2}b^{2} & ab & a + b \end{matrix} \right|$ is equal to

• A. abc
• B. a²b²c²
• C. ab + bc + ca
• D. None

Answer 1

Answer: (D)

None

Answer 2

$\frac{1}{abc}\left| \begin{matrix} ab^{2}c^{2} & abc & ab + ac \\ bc^{2}a^{2} & bca & bc + ba \\ ca^{2}b^{2} & cab & ca + cb \end{matrix} \right|$

=$\frac{(abc)^{2}}{abc}\left| \begin{matrix} bc & 1 & ab + ac \\ ca & 1 & bc + ba \\ ca & 1 & ca + cb \end{matrix} \right|$ = 0

(Now applying C₃ ® C₃ + C₁ and taking common

ab + bc + ac)