Solve the following determinant equations: 3x-8&3&3 3&3x-8&8 3&3&… - Vidyadip

Question

Solve the following determinant equations:
$\begin{vmatrix}3\text{x}-8&3&3\\3&3\text{x}-8&8\\3&3&3\text{x}-8\end{vmatrix}=0$

✓

Answer

$\begin{vmatrix}3\text{x}-8&3&3\\3&3\text{x}-8&8\\3&3&3\text{x}-8\end{vmatrix}=0$
Apply $\mathrm{C}_1 \rightarrow \mathrm{C}_1+\mathrm{C}_2+\mathrm{C}_3$
$\Rightarrow\begin{vmatrix}3\text{x}-2&3&3\\3\text{x}-2&3\text{x}-8&8\\3\text{x}-2&3&3\text{x}-8\end{vmatrix}=0$
$\Rightarrow(3\text{x}-2)\begin{vmatrix}1&3&3\\1&3\text{x}-8&8\\1&3&3\text{x}-8\end{vmatrix}=0$
$\Rightarrow(3\text{x}-2)\begin{vmatrix}1&3&3\\0&3\text{x}-11&0\\0&0&3\text{x}-11\end{vmatrix}=0$
$\Rightarrow(3\text{x}-2)(3\text{x}-11)^2=0$
$\Rightarrow(3\text{x}-2)=0$ or $(3\text{x}-11)^2=0$
$\Rightarrow\text{x}=\frac{2}{3}$ or $\text{x}=\pm\frac{11}{3}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "5 Marks Questions" from Determinants→Determinants — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Evaluate the following intregals:
$\int\frac{1}{\text{x}\log\text{x}(2+\log\text{x})}\text{ dx}$

Integrate the function in Exercise:
$\frac{5\text{x}+3}{\sqrt{\text{x}^2+4\text{x}+10}}$

Solve the following systems of linear equations by cramer's rule:

Differentiate the following functions with respect to x:
$\log(\text{cosec x}-\cot\text{x})$

Show that $\text{f(x)}=\begin{cases}12\text{x}-13, & \text{if x}\leq3\\2\text{x}^2+5, & \text{if x} > 3\end{cases}$ is differentiable at x = 3. Also, find f(3).

Evaluate the following integrals:
$\int\limits^{1}_0\frac{\log(1+\text{x})}{1+\text{x}^2}\text{ dx}$

A square piece of tin of side $18\ cm$ is to be made into a box without top by cutting a square from each corner and folding up the flaps to form a box. What should be the side of the square to be cut off so that the volume of the box is maximum? Find this maximum volume.

Find the angle between the line joining the points (3, -4, -2) and (12, 2, 0) and the plane 3x - y + z = 1.

A unit vector $\vec{\text{a}}$ makes angles $\frac{\pi}{4}$ and $\frac{\pi}{3}$ with $\hat{\text{i}}$ and $\hat{\text{j}}$ respectively and an acute angle $\theta$ with $\hat{\text{k}}$. find the angle $\theta$ and components of $\vec{\text{a}}$ .

Show the solution zone of the following inequalities on a graph paper:
$\text{x}+\text{y}\leq50$
$3\text{x}+\text{y}\geq90$
$\text{x},\text{y}\geq0$