I try to understand math for 3D games.

If I want to translate a point, I may do it in two ways:  

1. Using vector summation.  

2. Using matrix multiplication.

For example:
Initial vector $p =(1,2,3)$.   
has to be translated by $t=(4,5,-6)$.  

$p + a = p2 => (1+4, 2+5, 3-6) = (5,7,-3)$.

If I want to complete "undo", I may $p3 = p2 + (-a)$ ,  

The math is simple.

But in books people often use matrix multiplication  

![from wiki](https://i.stack.imgur.com/xKYOv.png)

For me it seems like doing much more computation.

I wonder, why do people use 4x4 matrix to do the same thing?