1. Tardigrade
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  3. Mathematics
  4. If I=[1&0 0&1], J=[0&1 -1&0] and B=[cos θ&sin θ - sin θ cos θ ], then B is equal to

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Q. If $I=\begin{bmatrix}1&0\\ 0&1\end{bmatrix}, J=\begin{bmatrix}0&1\\ -1&0\end{bmatrix}$ and $B=\begin{bmatrix}cos\,\theta&sin\,\theta \\ -\sin\,\theta &\cos\,\theta \end{bmatrix}, $ then $B$ is equal to

VITEEEVITEEE 2011Determinants

Solution:

$B=\begin{bmatrix}\cos \theta & \sin \theta \\ -\sin \theta & \cos \theta\end{bmatrix}$
$=\begin{bmatrix}\cos \theta & 0 \\ 0 & \cos \theta\end{bmatrix}+\begin{bmatrix}0 & \sin \theta \\ -\sin \theta & 0\end{bmatrix}$
$=\cos \theta\begin{bmatrix}1 & 0 \\ 0 & 1\end{bmatrix}+\sin \theta\begin{bmatrix}0 & 1 \\ -1 & 0\end{bmatrix}$
$=I \cos \theta+J \sin \theta$