Let F( ) = [ * 20 c & - &0 & &0 0&0&1 ], where R. Then [F( )]^ - … - Vidyadip

MCQ

Let $F(\alpha ) = \left[ {\begin{array}{*{20}{c}}{\cos \alpha }&{ - \sin \alpha }&0\\{\sin \alpha }&{\cos \alpha }&0\\0&0&1\end{array}} \right]$, where $\alpha \in R.$ Then ${[F(\alpha )]^{ - 1}}$ is equal to

✓
$F( - \alpha )$
B
$F({\alpha ^{ - 1}})$
C
$F(2\alpha )$
D
None of these

✓

Answer

Correct option: A.

$F( - \alpha )$

a
(a) We have

$F(\alpha )\,F( - \alpha )\, = \,\left[ {\begin{array}{*{20}{c}}{\cos \alpha }&{ - \sin \alpha }&0\\{\sin \alpha }&{\cos \alpha }&0\\0&0&1\end{array}} \right]\,\,\left[ {\begin{array}{*{20}{c}}{\cos \alpha }&{\sin \alpha }&0\\{ - \sin \alpha }&{\cos \alpha }&0\\0&0&1\end{array}} \right]$

= $\left[ {\begin{array}{*{20}{c}}1&0&0\\0&1&0\\0&0&1\end{array}} \right] = I$

$\therefore $ $F( - \alpha ) = {[F(\alpha )]^{ - 1}}$.

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 "M.C.Q (1 Marks)" from STD 12 - 3 and 4 . determinant and metrices→STD 12 - 3 and 4 . determinant and metrices — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

The value of the limit $\lim _{n \rightarrow \infty} \int \limits_0^1 x^{10} \sin (n x) d x$ equals

Let $a = 2i - j + k,\,\,b = i + 2j - k$ and $c = i + j - 2k$ be three vectors. A vector in the plane of $ b $ and $c $ whose projection on $a$ is of magnitude $\sqrt {2/3} $ is

Let $f(x) = \int\limits_1^x {\frac{{{{\tan }^{ - 1}}t}}{t}} dt\,(X > 0)$ then $f({e^2}) - f\left( {\frac{1}{{{e^2}}}} \right)$ is

Let $\quad \vec{a}=9 \hat{i}-13 \hat{j}+25 \hat{k}, \vec{b}=3 \hat{i}+7 \hat{j}-13 \hat{k} \quad$ and $\overrightarrow{\mathrm{c}}=17 \hat{\mathrm{i}}-2 \hat{\mathrm{j}}+\hat{\mathrm{k}}$ be three given vectros. If $\overrightarrow{\mathrm{r}}$ is a vector such that $\vec{r} \times \vec{a}=(\vec{b}+\vec{c}) \times \vec{a}$ and $\vec{r} .(\vec{b}-\vec{c})=0$, then $\frac{|593 \vec{r}+67 \vec{a}|^2}{(593)^2}$ is equal to...........

A biased coin with probabilty p, 0 < p < 1, of heads is tossed until a head appears for the first time. If the probability that the number of tosses required is even is $\frac{2}{5},$ then p equals:

The value of the integral $\int_{-1}^2 \log _e\left(x+\sqrt{x^2+1}\right) d x$ is:

The option$(s)$ with the values of $a$ and $L$ that satisfy the following equation is(are) $\frac{\int_0^{4 \pi} e^t\left(\sin ^6 a t+\cos ^4 a t\right) d t}{\int_0^\pi e^t\left(\sin ^6 a t+\cos ^4 a t\right) d t}=L ?$

$(A)$ $a=2, L=\frac{e^{4 \pi}-1}{e^\pi-1}$ $(B)$ $a=2, L=\frac{e^{4 \pi}+1}{e^\pi+1}$

$(C)$ $a=4, L=\frac{e^{4 \pi}-1}{e^\pi-1}$ $(D)$ $a=4, L=\frac{e^{4 \pi}+1}{e^\pi+1}$

The binary operation $\times$ defined on $N$ by $a \times b = a + b + ab$ for all $a, b \in N$ is:

Let $A=\left(\begin{array}{cc}1 & 2 \\ -2 & -5\end{array}\right)$. Let $\alpha, \beta \in R$ be such that $\alpha A^{2}+\beta A=2 I$. Then $\alpha+\beta$ is equal to -

The function $\text{f(x)}=|\cos\text{x}|$ is: