Download App

Determinants — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSDeterminants5 Marks
Question
Without expanding, show that the values of the following determinant are zero:
$\begin{vmatrix}\text{a}&\text{b}&\text{c}\\\text{a}+2\text{x}&\text{b}+2\text{y}&\text{c}+2\text{z}\\\text{x}&\text{y}&\text{z}\\\end{vmatrix}$
✓

Answer

$\triangle=\begin{vmatrix}\text{a}&\text{b}&\text{c}\\\text{a}+2\text{x}&\text{b}+2\text{y}&\text{c}+2\text{z}\\\text{x}&\text{y}&\text{z}\\\end{vmatrix}$
$=\begin{vmatrix}\text{a}+2\text{x}&\text{b}+2\text{y}&\text{c}+2\text{z}\\\text{a}+2\text{x}&\text{b}+2\text{y}&\text{c}+2\text{z}\\\text{x}&\text{y}&\text{z}\end{vmatrix} [$Applying $R_1 \rightarrow R_1 + 2R_3]$
 $=\begin{vmatrix}0&0&0\\\text{a}+2\text{x}&\text{b}+2\text{y}&\text{c}+2\text{z}\\\text{x}&\text{y}&\text{z}\end{vmatrix}=0[$ Applying $R_1 \rightarrow R_1 + R_2]$

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→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

Two schools $P$ and $Q$ want to award their selected students on the values of Tolerance, Kindness, and Leade $Rs$ .hip. The school $P$ wants to award $Rs. x$ each, $Rs. y$ each and $Rs. z$ each for the three respective values to $3, 2 $ and $1$ students respectively with total award money of $Rs.2200$.
School $Q$ wants to spend $Rs.. 3100$ to award its $4, 1$ and $3$ students on the respective values $($by giving the sameaward money to the three values as school $P)$. If the total amount of award for one prize on each value is $Rs.1200,$ using matrices, find the award money for each value
→
Evaluate the following intregals:
$\int\frac{1}{5-4\cos\text{x}}\ \text{dx}$
→
A card from a pack of $52$ cards is lost. From the remaining cards of the pack, two cards are drawn and are found to be both diamonds. Find the probability of the lost card being a diamond.
→
The population of a city increases at a rate proportional to the number of inhabitants present at any time t. If the population of the city was 200000 in 1990 and 250000 in 2000, what will be the population in 2010?
→
Solve the following systems of linear equations by cramer's rule:
2x - y = -2,
3x + 4y = 3
→
Find the derivative of the function $f(x)$ given by $f(x) = (1 + x) (1 + x^2) (1 + x^4) (1 + x^8)$ and hence find $f(1).$
→
If A and B are independent events such that P(A) = p, P(B) = 2p and P(Exactly one of A and B occurs) $=\frac{5}{9},$ then find the value or p.
→
If the product of the distances of the point $(1, 1, 1)$ from the origin and the plane $x - y + z + \lambda = 0$ be $5,$ find the value of $\lambda .$
→
Verify Lagrange's mean value theorem for the following function on the indicated intervals. find a point 'c' in the indicated interval as stated by the Lagrange's mean value theorem.
$\text{f}(\text{x})=\tan^{-1}\text{x}\text{ on }[0,1]$
→
Evaluate the following integrals:
$\int\frac{1}{(\text{x}^2+2\text{x}+10)^2}\text{ dx}$
→