Camera Extrinsics are used to represent a point in the world coordinate frame \(\{o\}\) in terms of the camera coordinate frame\(\{k\}\). To get the camera extrinsics matrix we need the [Orientation] of the camera with respect to \(\{o\}\) given as \(^o_kR\) and the [Position] of the origin of \(\{k\}\) with respect to \(\{o\}\) given as \(^oP_{korg}\). Therefore the transformation matrix from world to camera frame will be given as
\[^kH_o = \begin{bmatrix} ^o_kR^T && -^o_kR^{T}{^oP_{korg}} \\ 0 && 1 \end{bmatrix}\]See [Coordinate Frame Transform] for proof.
The camera extrinsic matrix changes as the camera moves around in the world because the orientation and the position of the origin of the camera center with respect to the world will also change.