Download App

DETERMINANTS — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDETERMINANTS2 Marks
Question
Without expanding, show that the values of the following determinant are zero:
$\begin{vmatrix}8&2&7\\12&3&5\\16&4&3 \end{vmatrix}$
✓

Answer

$\triangle=\begin{vmatrix}8&2&7\\12&3&5\\16&4&3 \end{vmatrix}$
$\Rightarrow\triangle=\begin{vmatrix}0&2&7\\12&3&5\\16&4&3 \end{vmatrix}$ [Applying $C_1 → C_1 - 4C_2$]
$\Rightarrow\triangle=0$

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 "2 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

For the principal values, evaluate the following:
$\tan^{-1}\Big\{2\sin\Big(4\cos^{-1}\frac{\sqrt3}{2}\Big)\Big\}$
→
A = {1, 2, 3, 4, 5, 6, 7, 8} and if R = {(x, y): y is one half of x; x, y ∈ A} is a relation on A, then write R as a set of ordered pairs.
→
Two cards are drawn without replacement from a pack of 52 cards. Find the probability that.
Both are kings.
→
Two cards are drawn at random and without replacement from a pack of 52 playing cards. Find the probability that both the cards are black.
→
Find the second order derivatives of the function given in Exercise:
$\text{e}^{6\text{x}}\cos3\text{x}$
→
For the principal values of the following:
$\cot^{-1}\Big(\sqrt3\Big)$
→
Write the component of $\vec{\text{b}}$ along $\vec{\text{a}}.$
→
Show that the Modulus Function f : R $\rightarrow$ R, given by f(x) = |x|, is neither one-one nor onto, where |x| is x, if x is positive or 0 and |x| is -x, if x is negative.
→
If $\vec{\text{a}}=\hat{\text{i}}+3\hat{\text{j}}-2\hat{\text{k}}$ and $\vec{\text{b}}=-\hat{\text{i}}+3\hat{\text{k},}$ find $\big|\vec{\text{a}}\times\vec{\text{b}}\big|.$
→
Evaluate the following integrals:
$\int\limits^3_0\frac{1}{\text{x}^2+9}\text{ dx}$
→