How is the rotation matrix of camera generated?

[grashin]

I'm trying to understand how xml file generates rotation matrix for camera.
I know that in the XML file, the camera data is represented as
r11, r12, r13, t1
r21, r22, r23, t2
r31, r32, r33, t3
0, 0, 0, 1

(t1 t2 t3) - 3D position of camera
R - camera rotation matrix
The camera is supposed to be looking at the center (c1, c2, c3)
And there is a approach named 'The Look-At Camera' to find rotation matrix from center point, camera point and up vector. But I couldn't get the rotation matrix from these two points and up vector (0, 1, 0).
Or is it a wrong assumption, that camera looking at the center, then how is the rotation matrix generated?