Easy Determinants??

Algebra Level 4

The value of

$\huge{\left| \begin{matrix} cos(\theta +\phi ) & -sin(\theta +\phi ) & cos2\phi \\ sin\theta & cos\theta & sin\phi \\ -cos\theta & sin\theta & \lambda cos\phi \end{matrix} \right| }$

$is$

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dependent on

\theta

\phi

and

\lambda

independent of

\phi

and

\lambda

independent of

\lambda

independent of

\theta

None independent of all variables

2 solutions

Tanishq Varshney
Mar 15, 2015

its simple

$R_{1} \rightarrow R_{2}sin(\phi)+R_{1}$

then

$R_{1} \rightarrow R_{3}cos(\phi)+R_{1}$

u will get final answer as $(\lambda+1) cos^{2}(\phi)$

yep or simply differentiate it with respect to theta and get that zero!

aryan goyat - 4 years, 6 months ago

Sourabh Jangid
Dec 29, 2016

*JUST SIMPLY OPEN IT WITH RESPECT TO THIRD COLUMN *

Easy Determinants??

2 solutions

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