If $E\left( \theta \right) = \left[ {\begin{array}{*{20}{c}} {{{\cos }^2}\theta }&{\cos \theta }&{\sin \theta }\\ {\cos \theta }&{\sin \theta }&{{{\sin }^2}\theta } \end{array}} \right]$ and ${\rm{\theta \;and\;}}\phi $ differ by an odd multiple of $\frac{\pi }{2},\;{\rm{then}}\;E\left( {\rm{\theta }} \right)$ $\;E\left( \emptyset \right)$ is a

JEE MATHEMATICS MCQ: MATRICES

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Application +4 | -1

E\left( \theta \right) = \left[ {\begin{array}{cccccccccccccccccccc} {{{\cos }^2}\theta }&{\cos \theta }&{\sin \theta }\\ {\cos \theta }&{\sin \theta }&{{{\sin }^2}\theta } \end{array}} \right]

and

\mathrm{\theta \;and\;}\phi

differ by an odd multiple of

\frac{\pi }{2},\;\mathrm{then}\;E\left( \mathrm{\theta } \right)

\;E\left( \emptyset \right)

is a

View answer and explanation

Correct option: B

Null matrix

The correct answer is Null matrix because when

\theta

and

\phi

differ by an odd multiple of

\frac{\pi}{2}

E(\theta)E(\phi)

results in a zero matrix.

Practice All Chapter MCQs →

\left|\begin{array}{ccc}a & b-c & b+c \\ c+a & b & c-a \\ a-b & a+b & c\end{array}\right|=0

a, b, c

a x+b y+c=0

{x_2} - {x_3} = 1,\; - {x_1} + 2{x_3} = - 2,\;{x_1} - 2,\;{x_1} - 2{x_2} = 3

2x + 3y + 1 = 0,3x + y - 2 = 0

ax + 2y - b = 0

\left|\begin{array}{ccc}1 & \left(\alpha^{2 x}-\alpha^{-2 x}\right)^2 & \left(\alpha^{2 x}+\alpha^{-2 x}\right)^2 \\ 1 & \left(\beta^{2 x}-\beta^{-2 x}\right)^2 & \left(\beta^{2 x}+\beta^{-2 x}\right)^2 \\ 1 & \left(\gamma^{2 x}-\gamma^{-2 x}\right)^2 & \left(\gamma^{2 x}+\gamma^{-2 x}\right)^2\end{array}\right|

\omega

\left| {\begin{array}{cccccccccccccccccccc} 1&\omega &{{\omega ^2}}\\ \omega &{{\omega ^2}}&1\\ {{\omega ^2}}&1&\omega \end{array}} \right|

A

2 \times 2

A(\operatorname{adj} A)=\left[\begin{array}{cc}10 & 0 \\ 0 & 10\end{array}\right]

|A|