Download App

Determinants — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsDeterminants3 Marks
Question
Write the value of the determinant $\begin{vmatrix}\text{x}+\text{y}&\text{y}+\text{z}&\text{z}+\text{x}\\\text{z}&\text{x}&\text{y}\\-3&-3&-3 \end{vmatrix}$
✓

Answer

$\begin{vmatrix}\text{x}+\text{y}&\text{y}+\text{z}&\text{z}+\text{x}\\\text{z}&\text{x}&\text{y}\\-3&-3&-3 \end{vmatrix}$
$=\begin{vmatrix}\text{x}+\text{y}+\text{z}&\text{x}+\text{y}+\text{z}&\text{z}+\text{x}+\text{y}\\\text{z}&\text{x}&\text{y}\\-3&-3&-3 \end{vmatrix}$ [Applying $R_1 \rightarrow R_1 + R_2$]
$=(\text{x}+\text{y}+\text{z})\begin{vmatrix}1&1&1\\\text{z}&\text{x}&\text{y}\\-3&-3&-3 \end{vmatrix}$ [Taking (x + y + z) common from $R_1$]
$=(\text{x}+\text{y}+\text{z})\begin{vmatrix}1&1&1\\\text{z}&\text{x}&\text{y}\\0&0&0 \end{vmatrix}$
$=0$ [Expanding along the last row]
Hence, the value of the determinant $\begin{vmatrix}\text{x}+\text{y}&\text{y}+\text{z}&\text{z}+\text{x}\\\text{z}&\text{x}&\text{y}\\-3&-3&-3 \end{vmatrix}$ is 0

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 "Solve the Following Question.(3 Marks)" from Determinants→Determinants — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

Differential equation $\frac{\text{d}^2\text{y}}{\text{dx}^2}+\text{y}=0,\text{y}(0)=0,\text{y}'(0)=1$Function $\text{y}=\sin\text{x}$
→
A coin is tossed 5 times. If X is the number of heads observed, find the probability distribution of X.
→
In $\triangle A B C$ prove that $a^2\left(\cos ^2 B-\cos ^2 C\right)+b^2\left(\cos ^2 C-\cos ^2 A\right)+c^2\left(\cos ^2 A-\cos ^2 B\right)=0$.
→
Write the following in the simplest form:
$\sin^{-1}\Big\{\frac{\sqrt{1+\text{x}}+\sqrt{1-\text{x}}}{2}\Big\},0<\text{x}<1$
→
How many times must a man toss a fair coin so that the probability of having at least one head is more than 80%?
→
A wire of length $l$ is cut into two parts. One part is bent into a circle and other into a square. Show that the sum of areas of the circles and squares is the least, if the radius of circle is half the side of the squares.
→
Find two unit vectors each of which is perpendicular to both

$\bar{u}$ and $\bar{v}_{\text {, where }} \bar{u}=2 \hat{i}+\hat{j}-2 \hat{k}, \bar{v}=\hat{i}+2 \hat{j}-2 \hat{k}$

→
Solve the following equation for x:
$\tan^{-1}(\text{x}+1)+\tan^{-1}(\text{x}-1)=\tan^{-1}\frac{8}{31}$
→
Evaluate the following integrals:$\int_{\pi}^\limits{\frac{3\pi}{2}}\sqrt{1-\cos2\text{x}}\text{ dx}$
→
Construct the composition table for $\times _6$​​​​​​​ on set $S = {0, 1, 2, 3, 4, 5}$.
→