Question

A=((cosθ&sinθ@-sinθ&cosθ)) எனில் AA^T=1 என காட்டுக

Answer 1

Answer:

$\sin {}^{2} \alpha + \cos { \beta}^{2} = 1$

Answer 2

விளக்கம்:

$A =\left[\begin{array}{cc}\cos \theta & \sin \theta \\-\sin \theta & \cos \theta\end{array}\right]$

நிருபிக்கவேண்டியவை

$A A^{T}= 1$

$A=\left[\begin{array}{cc}\cos \theta & \sin \theta \\-\sin \theta & \cos \theta\end{array}\right]$

$A^{T}=\left|\begin{array}{cc}\cos \theta & -\sin \theta \\\sin \theta & \cos \theta\end{array}\right|$

$AA^T=\left[\begin{array}{ccc}\cos \theta & \sin \theta \\-\sin \theta & \cos \theta\end{array}\right]\left[\begin{array}{cc}\cos \theta & -\sin \theta \\\sin \theta & \cos \theta\end{array}\right]$

       $= \left[\begin{array}{ll}1 & 0 \\0 & 1\end{array}\right]$  

        = 1 = I

$A A^{T}= 1$ என நிருபிக்கபட்டது.