I have the following problem. Does anyone know how to start with? Any links on what to read in order to understand what I have to do?
Which of the following transformations map the points $t_0=(-1,-1,-1)^T,t_1=(1,1,-1)^T$, $t_2=(-1,1,1)^T$, and $t_3=(1,-1,1)^T$ of the tetrahedron $T$ to the points $u_0=(2,2,-1)^T$, $u_1=(2,2,3)^T,u_2=(0,0,1)^T$, and $u_3=(4,0,1)^T$ (i.e. map $t_i$ to $u_i$ for $i=0,1,2,3$)?
- Rotation about the $z$-axis by $45^\circ$, then scaling with $s_x=\sqrt2,s_y=\sqrt2,s_z=1$, then translation by $(2,1,-1)$, and then rotation about the $x$-axis by $90^\circ$.
- Rotation about the $x$-axis by $90^\circ$, then scaling with $s_x=\sqrt2,s_y=1,s_z=\sqrt2$, then rotation about the $y$-axis by $45^\circ$, and then translation by $(2,1,1)$.
- Translation by $(1,-1,2)$, then rotation about the $z$-axis by $45^\circ$, then scaling with $s_x=\sqrt2,s_y=\sqrt2,s_z=1$, and then rotation about the $x$-axis by $90^\circ$.
- Scaling with $s_x=\sqrt2,s_y=\sqrt2,s_z=1$, then rotation about the $z$-axis by $45^\circ$, then translation by $(2,1,-1)$, and then rotation about the $x$-axis by $90^\circ$.
- Rotation about the $x$-axis by $90^\circ$, then rotation about the $y$-axis by $45^\circ$, then translation by $(1,1,\sqrt{1/2})$, and then scaling with $s_x=2,s_y=1,s_z=\sqrt2$.
Any help would be grateful.