If F( ) = [ * 20 c & - &0 & &0 0&0&1 ] and G ,( ) = [ * 20 c &0& … - Vidyadip

MCQ

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

A
$F(\alpha )\, - G(\beta )$
B
$ - F(\alpha )\, - G(\beta )$
C
${[F(\alpha )]^{ - 1}}\,{[G(\beta )]^{ - 1}}$
✓
${[G(\beta )]^{ - 1}}{[F(\alpha )]^{ - 1}}$

✓

Answer

Correct option: D.

${[G(\beta )]^{ - 1}}{[F(\alpha )]^{ - 1}}$

d
(d) Since ${(AB)^{ - 1}} = {B^{ - 1}}{A^{ - 1}}$.

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 3 and 4 . determinant and metrices→3 and 4 . determinant and metrices — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

The area of the region bounded by the curve $\text{y}=\sin\text{x}$ between the ordinates $\text{x}=0,\text{x}=\frac{\pi}{2}$ and the x-axis is:

2 sq. units
4 sq. units
3 sq. units
1 sq. unit

Let $f (x)$ be diffrentiable at $x = h$ then $\mathop {\lim }\limits_{x \to h} \,\frac{{(x + h)\,f(x)\, - 2h\,f(h)}}{{x - h}}$ is equal to

The area bounded by $x^2 + y^2 - 2 x = 0\,\, \&\,\, y = \sin \frac{{\pi \,x}}{2}$ in the upper half of the circle is :

If area of triangle is 35 sq. units with vertices $(2,-6),(5,4)$ and $(k, 4)$, then $k=$ _________ .

The vector a coplanar with the vectors $ i $ and $j$ , perpendicular to the vector $b = 4i - 3j + 5k$ such that $|a|\, = \,|\,b|$ is

Let $A$ be a square matrix such that $A A^T=I$. Then $\frac{1}{2} A\left[\left(A+A^T\right)^2+\left(A-A^T\right)^2\right]$ is equal to

Let $\alpha$ be the area of the larger region bounded by the curve $y ^2=8 x$ and the lines $y = x$ and $x =2$, which lies in the first quadrant. Then the value of $3 \alpha$ is equal to $..............$.

Considering only the principal values of inverse trigonometric functions, the number of positive real values of $x$ satisfying $\tan ^{-1}(x)+\tan ^{-1}(2 x)=\frac{\pi}{4}$ is:

Choose the correct answer from the given four option.
Integrating factor of the differential equation $\cos\frac{\text{d}\text{y}}{\text{d}\text{x}}+\text{y}\sin\text{x}=1$ is:

$\cos\text{x}$
$\tan\text{x}$
$\sec\text{x}$
$\sin\text{x}$

The system of linear equations $x + y + z = 2$, $2x + y - z = 3,$ $3x + 2y + kz = 4$has a unique solution if