Class 12Mathematics3-4. Matrices and DeterminantsExpansion of determinants, Solution of equation in the form of determinants and area of triangle and Equation of Line
MediumEvaluate $\left|\begin{array}{ccc}1 & x & y \\ 1 & x+y & y \\ 1 & x & x+y\end{array}\right|$
- A$xy$
- B$x^2y$
- C$x^2y^2$
- D$xy^2$
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$\left|\begin{array}{ccc} \log e & \log e^2 & \log e^3 \\ \log e^2 & \log e^3 & \log e^4 \\ \log e^3 & \log e^4 & \log e^5 \end{array}\right| \text{ is equal to: }$
If ${\Delta _1} = \left| {\begin{array}{*{20}{c}}1&0\\a&b\end{array}} \right|$ and ${\Delta _2} = \left| {\begin{array}{*{20}{c}}1&0\\c&d\end{array}} \right|$,then ${\Delta _2}{\Delta _1}$ is equal to
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View SolutionIf $x^2+y^2+z^2 \neq 0, \quad x=cy+bz, \quad y=az+cx$ and $z=bx+ay$, then $a^2+b^2+c^2+2abc$ is equal to
If $2\left|\begin{array}{ll}\sin ( A + B ) & \cos ( A + B ) \\ \cos ( A - B ) & \sin ( A - B )\end{array}\right|+\sqrt{3}= 0$,then $A =$ . . . . . . .
$\left|\begin{array}{cc}\sin \frac{2 \pi}{9} & \cos \frac{2 \pi}{9} \\ \sin \frac{5 \pi}{18} & \cos \frac{5 \pi}{18}\end{array}\right|=$ . . . . . . .
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