Download App

Matrices — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSMatrices1 Mark
Question
If $A=\left[\begin{array}{rr}\cos \alpha & -\sin \alpha \\ \sin \alpha & \cos \alpha\end{array}\right]$, then for what value of $\alpha, A$ is an identity matrix?
✓

Answer

(a) : $A=\left[\begin{array}{rr}\cos \alpha & -\sin \alpha \\ \sin \alpha & \cos \alpha\end{array}\right]$ is an identity matrix if, $\left[\begin{array}{rr}\cos \alpha & -\sin \alpha \\ \sin \alpha & \cos \alpha\end{array}\right]=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]$
$\therefore \cos \alpha=1$ and $\sin \alpha=0 \Rightarrow \alpha=0^{\circ}$.

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 Matrices→Matrices — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

If x, y, z are non-zero real numbers, then the inverse, then the inverse of the matrix $\begin{bmatrix}\text{x} & 0 & 0\\ 0 & \text{y} & 0 \\ 0 & 0 & \text{z}\end{bmatrix}$, is:
  1. $\begin{bmatrix}\text{x}^{-1} & 0 & 0\\ 0 & \text{y}^{-1} & 0 \\ 0 & 0 & \text{z}^{-1}\end{bmatrix}$
  2. $\text{xyz}\begin{bmatrix}\text{x}^{-1} & 0 & 0\\ 0 & \text{y}^{-1} & 0 \\ 0 & 0 & \text{z}^{-1}\end{bmatrix}$
  3. $\frac{1}{\text{xyz}}\begin{bmatrix}\text{x} & 0 & 0\\ 0 & \text{y} & 0 \\ 0 & 0 & \text{z}\end{bmatrix}$
  4. $\frac{1}{\text{xyz}}\begin{bmatrix} 1 & 0 & 0\\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}$
→
The area bounded by the curve $2x^2 + y^2 = 2$ is$:$
→
If for a square matrix A, A.(adjA) $=\left[\begin{array}{ccc}2025 & 0 & 0 \\ 0 & 2025 & 0 \\ 0 & 0 & 2025\end{array}\right]$ then the value of $|A|+|a d j A |$ is equal to.
→
In a $\triangle\text{ABC},$ if C is a right angle, then $\tan^{-1}\Big(\frac{\text{a}}{\text{b}+\text{c}}\Big)+\tan^{-1}\Big(\frac{\text{b}}{\text{c}+\text{b}}\Big)=$
  1. $\frac{\pi}{3}$
  2. $\frac{\pi}{4}$
  3. $\frac{5\pi}{2}$
  4. $\frac{\pi}{6}$
→
Let $R$ be the relation on the set of all real numbers defined by $a R b$ iff $|a-b| \leq 1$. Then, $R$ is
→
$\cos ^{-1}\left(\frac{\sqrt{3}}{2}\right)=$
→
If the curve $ay + x^2 = 7$ and $x^3 = y$ cut orthogonally at $(1, 1)$, then a is equal to:
→
Maximize $Z=7 x+11 y$, subject to $3 x+5 y \leq 26$, $5 x+3 y \leq 30, x \geq 0, y \geq 0$.
→
If there is an error of a% in measuring the edge of a cube, then percentage error in its surface is:
  1. 2a%
  2. $\frac{\text{a}}{2}\%$
  3. 3a%
  4. None of these
→
The number of all possible matrices of order $3\times 3$ with each entry $0$ or $1$ is$:$
→