Evaluate 2&3&7 13&17&5 15&20&12 ^2 - Vidyadip

Question

Evaluate $\begin{vmatrix}2&3&7\\13&17&5\\15&20&12\end{vmatrix}^2$

✓

Answer

Let $\text{A}=\begin{vmatrix}2&3&7\\13&17&5\\15&20&12\end{vmatrix}$
$\Rightarrow\text{A}=2(204-100)-3(156-75)+7(260-255)$
$\Rightarrow\text{A}=2(104)-3(81)+7(5)$
$\Rightarrow\text{A}=208-243+35$
$\Rightarrow\text{A}=243-243=0$
$\because\begin{vmatrix}2&3&7\\13&17&5\\15&20&12\end{vmatrix}=0$
$\Rightarrow\begin{vmatrix}2&3&7\\13&17&5\\15&20&12\end{vmatrix}^2=0^2=0$ $\big[\therefore\text{det } \text{A}^2 = (\text{det} \text{A})^2\big]$

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 "3 Marks Question" from DETERMINANTS→DETERMINANTS — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

Let $A = \{1, 2, 3\},$ and let $R_3 = \{(1, 3), (3, 3)\}.$ Find whether or not the relations $R_{3 }$ on $A$ is$:$

Reflexive.
Symmetric.
Transitive.

Find the shortest distance between lines $\vec{r}=6 \hat{i}+2 \hat{j}+2 \hat{k}+\lambda(\hat{i}-2 \hat{j}+2 \hat{k})$ and $\vec{r}=-4 \hat{i}-\hat{k}+\mu(3 \hat{i}-2 \hat{j}-2 \hat{k})$

Find the vector equation of the line passing through (1, 2, 3) and perpendicular to the plane $\vec{\text{r}}.\Big(\hat{\text{i}}+2\hat{\text{j}}-5\hat{\text{k}}\Big)+9=0.$

For what value of $k$ the following distribution is a probability distributioin?

$X = x_i$	$0$	$1$	$2$	$3$
$P(X = x_i)$	$2k^4$	$3k^2 - 5k^3$	$2k - 3k^2$	$3k - 1$

Discuss the applicability of the Rolle's theorem for the following function on the indicated interval
$\text{f}(\text{x})=\text{x}^{\frac{2}{3}}\text{ on }[-1,1]$

Find the area of the triangle with vertices at the points: $(3, 8), (-4, 2)$ and $(5, -1)$

$\int\frac{1}{\cos^2\text{x}(1-\tan\text{x})^2}\text{dx}$

Find the interval for which $f(x)=x^4-2 x^2$ is increasing or decreasing.

Write the minors and cofactors of element of the first column of the following matrices and hence evaluate the determinant in case:
$\text{A}=\begin{vmatrix}-1&4\\2&3 \end{vmatrix}$

$\int\frac{1}{\sqrt{\text{x+a}}+\sqrt{\text{x+b}}}\text{dx}$