Scaling Transformation

The scaling transformation matrix is defined like this.

\[\M{S}=\begin{bmatrix} \red{x} & 0 & 0 & 0 \\ 0 & \red{y} & 0 & 0 \\ 0 & 0 & \red{z} & 0 \\ 0 & 0 & 0 & 1 \\ \end{bmatrix}\] \[\begin{array}{ccccccccccl} w_x &=& v_x\cdot\red{x} &+& v_y\cdot 0 &+& v_z\cdot 0 &+& v_w\cdot 0 &=& v_x\cdot\red{x} \\ w_y &=& v_x\cdot 0 &+& v_y\cdot\red{y} &+& v_z\cdot 0 &+& v_w\cdot 0 &=& v_y\cdot\red{y} \\ w_z &=& v_x\cdot 0 &+& v_y\cdot 0 &+& v_z\cdot\red{z} &+& v_w\cdot 0 &=& v_z\cdot\red{z} \\ w_w &=& v_x\cdot 0 &+& v_y\cdot 0 &+& v_z\cdot 0 &+& v_w\cdot 1 &=& v_w \\ \end{array}\]