Decomposing Motions: Solving the T:R(4) to R(4) Question

[gezmisoguz]

Can anybody help me to solve this question?

Consider the motion T:R(4) to R(4) given by T(x,y,z,w)=(w+3,x,y,z+1) T as a composition of traslations, reflections and rotations.

 

[tiny-tim]

Welcome to PF!

Hi gezmisoguz! Welcome to PF!

Can anybody help me to solve this question?

Consider the motion T:R(4) to R(4) given by T(x,y,z,w)=(w+3,x,y,z+1) T as a composition of traslations, reflections and rotations.

Well, the obvious thing to do is to go via (w,x,y,z)

 

[gezmisoguz]

Thanks:)

I tried to use that but i can not reach translation rotation and reflection form of this.

Please give some hints to me:)

 

[HallsofIvy]

First step T(x,y,z,w)= (w, x, y, z)+ (3, 0, 0, 1). That (3, 0, 0, 1) is a translation.

Now, what is U(x,y,z,w)= (w, x, y, z)?

 

[gezmisoguz]

We must use a matrix to change basis of (w,x,y,z). Can this matrix contain rotation and reflection?

 

[Martin Rattigan]

Couldn't you have thought of a better title?

 

[HallsofIvy]

We must use a matrix to change basis of (w,x,y,z). Can this matrix contain rotation and reflection?

Well, what have you done on this? Have you written it as a matrix? What is the determinant of that matrix?