Question

If $y = \sin mx$, then the value of the determinant$\left| \begin{matrix} y & y_{1} & y_{2} \\ y_{3} & y_{4} & y_{5} \\ y_{6} & y_{7} & y_{8} \end{matrix} \right|$, where $y_{n} = \frac{d^{n}y}{dx^{n}}$ is

• A. $m^{9}$
• B. $m^{2}$
• C. $m^{3}$
• D. None of these

Answer 1

Answer: (D)

None of these

Answer 2

$\left| \begin{matrix} y & y_{1} & y_{2} \ y_{3} & y_{4} & y_{5} \ y_{6} & y_{7} & y_{8} \end{matrix} \right| = \left| \begin{matrix} \sin mx & m\cos mx & - m^{2}\sin mx \

• m^{3}\cos mx & m^{4}\sin mx & m^{5}\cos mx \
• m^{6}\sin mx & - m^{7}\cos mx & m^{8}\sin mx \end{matrix} \right|$Taking$- m^{6}$common from$R_{3},R_{1}$and$R_{3}$ becomes

identical. Hence the value of determinant is zero.