Evaluate the determinant | * 20 c 0&1&2 - 1 &0& - 3 - 2 &3&0 | - Vidyadip

Question

Evaluate the determinant $\left| {\begin{array}{*{20}{c}} 0&1&2 \\ { - 1}&0&{ - 3} \\ { - 2}&3&0 \end{array}} \right|$

✓

Answer

Given: $\left| {\begin{array}{*{20}{c}} 0&1&2 \\ { - 1}&0&{ - 3} \\ { - 2}&3&0 \end{array}} \right|$
Expanding along first row, $0\left| {\begin{array}{*{20}{c}} 0&{ - 3} \\ 3&0 \end{array}} \right| - 1\left| {\begin{array}{*{20}{c}} { - 1}&{ - 3} \\ { - 2}&0 \end{array}} \right| + 2\left| {\begin{array}{*{20}{c}} { - 1}&0 \\ { - 2}&3 \end{array}} \right|$
= 0(0 + 9) - (0 - 6) + 2( - 3 - 0)
= 0 + 6 - 6 = 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 "1 Marks Question" 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

Prove that the radius of the right circular cylinder of greatest curved surface area, which can be inscribed in a given cone, is half of that of the cone.

Determine order and degree (if defined) of differential equation ${\left( {\frac{{ds}}{{dt}}} \right)^4} + 3s\frac{{{d^2}s}}{{d{t^2}}} = 0$

Evaluate the following:
$\tan^{-1}\Big(\tan\frac{\pi}{3}\Big)$

Evaluate: $\int\limits_{2}^{4}\frac{\text{x}}{\text{x}^{2} +1}\text{dx}.$

Write the degree of the following differrntial equation?
$5\text{x}\Big(\frac{\text{dy}}{\text{dx}}\Big)^{2}-\frac{\text{d}^{2}\text{y}}{\text{dx}^{2}}-6\text{y}=\log\text{x}$

Two events A and B will be independent, if

What is the principal value of $\cot^{-1} \Bigg(\cos\frac{2\pi}{3}\Bigg)+\sin^{-1}\Bigg(\sin\frac{2\pi}{3}\Bigg)?$

Find the integral: $\int \frac{x+3}{\sqrt{5-4 x-x^{2}}} d x$

Prove that $ \cos ^ { - 1 } \left( \frac { 4 } { 5 } \right) + \cos ^ { - 1 } \left( \frac { 12 } { 13 } \right) = \cos ^ { - 1 } \left( \frac { 33 } { 65 } \right).$

The value of $\hat{i} \cdot(\hat{j} \times \hat{k})+\hat{j} \cdot(\hat{i} \times \hat{k})+\hat{k} \cdot(\hat{i} \times \hat{j})$ is