Question

The determinant $\left| \begin{matrix} ax & by & cz \\ x^{2} & y^{2} & z^{2} \\ 1 & 1 & 1 \end{matrix} \right|$ is equal to –

• A. $\left| \begin{matrix} 1 & 1 & 1 \\ a & b & c \\ x^{2} & y^{2} & z^{2} \end{matrix} \right|$
• B. $\left| \begin{matrix} a & b & c \\ x & y & z \\ yz & zx & xy \end{matrix} \right|$
• C. $\left| \begin{matrix} 1 & 1 & 1 \\ x & y & z \\ a^{2} & b^{2} & c^{2} \end{matrix} \right|$
• D. None of these

Answer 1

Answer: (B)

$\left| \begin{matrix} a & b & c \\ x & y & z \\ yz & zx & xy \end{matrix} \right|$

Answer 2

$\frac{1}{xyz}$ $\left| \begin{matrix} ax & by & cz \\ x^{2} & y^{2} & z^{2} \\ xyz & xyz & xyz \end{matrix} \right|$= $\frac{xyz}{xyz}$ $\left| \begin{matrix} a & b & c \\ x & y & z \\ yz & xz & xy \end{matrix} \right|$