Mark the tick against the correct answer in the following: The solution set of the equation $\left|\begin{array}{ccc}3 \mathrm{x}-8 & 3 & 3 \\ 3 & 3 \mathrm{x}-8 & 3 \\ 3 & 3 & 3 \mathrm{x}-8\end{array}\right|=0$ is A. $\left\{\frac{2}{3}, \frac{8}{3}\right\}$ B. $\left\{\frac{2}{3}, \frac{11}{3}\right\}$ C. $\left\{\frac{3}{2}, \frac{8}{3}\right\}$ D. None of these

Home » Mark the tick against the correct answer in the following: The solution set of the equation is A. B. C. D. None of these

Mark the tick against the correct answer in the following: The solution set of the equation $\left|\begin{array}{ccc}3 \mathrm{x}-8 & 3 & 3 \\ 3 & 3 \mathrm{x}-8 & 3 \\ 3 & 3 & 3 \mathrm{x}-8\end{array}\right|=0$ is
A. $\left\{\frac{2}{3}, \frac{8}{3}\right\}$
B. $\left\{\frac{2}{3}, \frac{11}{3}\right\}$
C. $\left\{\frac{3}{2}, \frac{8}{3}\right\}$
D. None of these

CBSE | Class 12 | Determinants | Maths | RS Aggarwal

Mark the tick against the correct answer in the following: The solution set of the equation $\left|\begin{array}{ccc}3 \mathrm{x}-8 & 3 & 3 \\ 3 & 3 \mathrm{x}-8 & 3 \\ 3 & 3 & 3 \mathrm{x}-8\end{array}\right|=0$ is
A. $\left\{\frac{2}{3}, \frac{8}{3}\right\}$
B. $\left\{\frac{2}{3}, \frac{11}{3}\right\}$
C. $\left\{\frac{3}{2}, \frac{8}{3}\right\}$
D. None of these

Solution:

Option(B)
To find: Value of $x$
We have, $\left|\begin{array}{ccc}3 x-8 & 3 & 3 \\ 3 & 3 x-8 & 3 \\ 3 & 3 & 3 x-8\end{array}\right|=0$
Applying $\mathrm{R}_{1} \rightarrow \mathrm{R}_{1}-\mathrm{R}_{2}$
$\Rightarrow\left|\begin{array}{ccc} 3 x-11 & 11-3 x & 0 \\ 3 & 3 x-8 & 3 \\ 3 & 3 & 3 x-8 \end{array}\right|=0$
Applying $\mathrm{R}_{2} \rightarrow \mathrm{R}_{2}-\mathrm{R}_{3}$
$\Rightarrow\left|\begin{array}{ccc} 3 x-11 & 11-3 x & 0 \\ 0 & 3 x-11 & 11-3 x \\ 3 & 3 & 3 x-8 \end{array}\right|=0$
Expanding along $R_{1}$
$\begin{array}{l} \Rightarrow(3 x-11)\{(3 x-11)(3 x-8)-(3)(11-3 x)\}-(11-3 x)\{(0)((3 x-8)-(11-3 x)(3)\}=0 \\ \Rightarrow(3 x-11)\{(3 x-11)(3 x-8+3)\}-(11-3 x)\{-(11-3 x)(3)\}=0 \\ \left.\Rightarrow(3 x-11)^{2}(3 x-5)\right\}+(3 x-11)\{(3 x-11)(3)\}=0 \\ \left.\left.\Rightarrow(3 x-11)^{2}(3 x-5)\right\}+(3 x-11)^{2}(3)\right\}=0 \\ \Rightarrow(3 x-11)^{2}(3 x-5+3)=0 \\ \Rightarrow(3 x-11)^{2}(3 x-2)=0 \\ \Rightarrow x=\frac{11}{3}, \text { Or, } x=\frac{2}{3} \end{array}$