Final transformation matrix to transform world coordinate into vrc For a 3D scene in the world coordinates, its View Reference Point $\mathrm{VRP}$ is at $(5,2,1)$, and a viewer is looking towards point $A=(1,1,1)$. Construct a transform matrix which will map  world  coordinate  points  to  a  right-handed  $(UVN)$  viewing  space,  so  that  VRP  is 
  the  origin,  the  line  joining  $\mathrm{VRP}$ to  $A$  is  the  positive  $N$  axis,  and  the  view-up  Vector  is $(0,0,1)$.  


I have calculated the translation matrix:

$$
T=
\begin{pmatrix}
1 &amp; 0 &amp; 0 &amp; -5 \\
0 &amp; 1 &amp; 0 &amp; 2 \\
0 &amp; 0 &amp; 1 &amp; -1 \\
0 &amp; 0 &amp; 0 &amp; 1 \\
\end{pmatrix}
$$

I have calculated the rotation matrix:

$$
R=
\begin{pmatrix}
-0.6 &amp; -0.8 &amp; 0 &amp; 0 \\
0 &amp; 0 &amp; 1 &amp; 0 \\
-0.8 &amp; 0.6 &amp; 0 &amp; 0 \\
0 &amp; 0 &amp; 0 &amp; 1 \\
\end{pmatrix}
$$

But what would the final transformation matrix $M$ be? My lecture slides tell me it would be rotation matrix multiplied by translation matrix, with the last column multiplied by $-1$ except for the $1$. This would equal:

$$
M = R \times T = 
\begin{pmatrix}
-0.6 &amp; -0.8 &amp; 0 &amp; -1.4 \\
0 &amp; 0 &amp; 1 &amp; 1 \\
-0.8 &amp; 0.6 &amp; 0 &amp; -5.2 \\
0 &amp; 0 &amp; 0 &amp; 1 \\
\end{pmatrix}
$$

But this answer here: Building view transform matrices

just adds them together somehow. Which one is correct?
Thanks for notification me, In my previous answer, I just combine the translation matrix and the rotation matrix, actually, It's the result translation matrix(T) multiply rotation matrix(R). 

The rotation is a 3x3 matrix, we can extend the matrix to a 4x4 matrix with adding a dimension, the 4x4 rotation matrix is:



And the translation matrix is:



So, now we can calculate the transform matrix by translation matrix multiply(T) rotation matrix(R):

Cause the matrix multiply formula is too big for the 4x4 matrix, we just look at the 1st row, In the transform matrix(M), the M11 element equals to T11*R11+T12*R21+T13*R31+T14*R41, cause T12, T13, R41 is 0, so, the M11 equals to R11 right? And in the same way, M14 equals to T11*R14+T12*R24+T13*R34+T14*R44, only R44 equals to 1, so, the M14 equals to T14. so, I just simply put them together in my last answer. For the reason why we put the translation matrix on the left, you can check on the book that I gave you in my previous answer on page 91(translating first and then rotating).