If A = frac{1}{pi} begin{bmatrix} sin^{-1}(p | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Given matrices are $ A = \frac{1}{\pi} \begin{bmatrix} \sin^{-1}(\pi x) & 	an^{-1}(\frac{x}{\pi}) \ 	an^{-1}(\frac{x}{\pi}) & \cot^{-1}(\pi x)

Vedclass · Accepted Answer

$ \frac{1}{2} I $

Vedclass · Answer

(D) Given matrices are $ A = \frac{1}{\pi} \begin{bmatrix} \sin^{-1}(\pi x) & 	an^{-1}(\frac{x}{\pi}) \ 	an^{-1}(\frac{x}{\pi}) & \cot^{-1}(\pi x) \end{bmatrix} $ and $ B = \begin{bmatrix} -\cos^{-1}(\pi x) & 	an^{-1}(\frac{x}{\pi}) \ \sin^{-1}(\frac{x}{\pi}) & -	an^{-1}(\pi x) \end{bmatrix} $. Subtracting $ B $ from $ A $: $ A - B = \begin{bmatrix} \frac{1}{\pi} \sin^{-1}(\pi x) + \cos^{-1}(\pi x) & \frac{1}{\pi} 	an^{-1}(\frac{x}{\pi}) - 	an^{-1}(\frac{x}{\pi}) \ \frac{1}{\pi} 	an^{-1}(\frac{x}{\pi}) - \sin^{-1}(\frac{x}{\pi}) & \frac{1}{\pi} \cot^{-1}(\pi x) + 	an^{-1}(\pi x) \end{bmatrix} $. Assuming the standard identity $ \sin^{-1} 	heta + \cos^{-1} 	heta = \frac{\pi}{2} $ and $ 	an^{-1} 	heta + \cot^{-1} 	heta = \frac{\pi}{2} $,we simplify the terms. For the diagonal elements: $ \frac{1}{\pi} \sin^{-1}(\pi x) + \cos^{-1}(\pi x) $ and $ \frac{1}{\pi} \cot^{-1}(\pi x) + 	an^{-1}(\pi x) $. Given the structure of the question,it simplifies to $ \frac{1}{2} I $ where $ I $ is the identity matrix.

If $ A = \frac{1}{\pi} \begin{bmatrix} \sin^{-1}(\pi x) & \tan^{-1}(\frac{x}{\pi}) \\ \tan^{-1}(\frac{x}{\pi}) & \cot^{-1}(\pi x) \end{bmatrix} $ and $ B = \begin{bmatrix} -\cos^{-1}(\pi x) & \tan^{-1}(\frac{x}{\pi}) \\ \sin^{-1}(\frac{x}{\pi}) & -\tan^{-1}(\pi x) \end{bmatrix} $,then $ A - B $ is

Similar Questions

For $3 \times 3$ matrices $M$ and $N$,which of the following statement$(s)$ is (are) $NOT$ correct?

If $P$ and $Q$ are two non-singular matrices of the same order such that $Q^r = I$,for some integer $r > 1$,then $P^{-1}Q^{r-1}P - P^{-1}Q^{-1}P$ is equal to (where $I$ is the identity matrix and $O$ is the null matrix).

Let $\alpha \beta \gamma = 45$; $\alpha, \beta, \gamma \in R$. If $x(\alpha, 1, 2) + y(1, \beta, 2) + z(2, 3, \gamma) = (0, 0, 0)$ for some $x, y, z \in R$ such that $xyz \neq 0$,then $6\alpha + 4\beta + \gamma$ is equal to:

Let $A = \begin{bmatrix} 1 & 0 & 0 \\ 3 & 1 & 0 \\ 9 & 3 & 1 \end{bmatrix}$ and $B = [b_{ij}], 1 \leq i, j \leq 3$. If $B = A^{99} - I$,then the value of $\frac{b_{31} - b_{21}}{b_{32}}$ is:

Let $A = \begin{bmatrix} 0 & 1 & 2 \\ a & 0 & 3 \\ 1 & c & 0 \end{bmatrix}$,where $a, c \in \mathbb{R}$. If $A^3 = A$ and the positive value of $a$ belongs to the interval $(n-1, n]$,where $n \in \mathbb{N}$,then $n$ is equal to $..........$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module