Question

If a, b, c are non-zero no.'s, 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 of these

Answer 1

Answer: (D)

None of these

Answer 2

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

=$\left| \begin{matrix} bc & 1 & ab + ac \\ ac & 1 & bc + ab \\ ab & 1 & ac + bc \end{matrix} \right|$= abc $\left| \begin{matrix} bc & 1 & ab + bc + ca \\ ac & 1 & ab + bc + ca \\ ab & 1 & ab + bc + ca \end{matrix} \right|$ = 0