1. If a certain transformation matrix M transforms 100100 to x1 y1 z1 010010 to x2 y2 z2 001001 to x3 y3 z3 Then, what is matrix M? Question : Direction Cosine

2. Solution : The above problem can be re-stated as such 100100 = M x1 y1 z1 100100 = M x2 y2 z2 100100 = M x3 y3 z3 In turn, if we put these 3 equations together,we can re- state it as follow : There, it is obvious that : = M x1 x2 x3 y1 y2 y3 z1 z2 z3 1 0 0 0 1 0 0 0 1 M = x1 x2 x3 y1 y2 y3 z1 z2 z3

3. If M transforms Then : 100100 to x1 y1 z1 010010 to x2 y2 z2 001001 to x3 y3 z3 Remember M = x1 x2 x3 y1 y2 y3 z1 z2 z3

4. What is the transformation matrix for R Z (  ) ? Question : Solution : 001001 to 001001 If R Z (  ) transforms 100100 to cos(  ) sin(  ) 0 010010 to -sin(  ) cos(  ) 0 R Z (  ) = cos(  ) - sin(  ) 0 sin(  ) cos(  ) 0 0 0 1 Then,

5. A (2,2,0) B Quick, if P A = M P B What is M? Solution : M = 0 1 0 2 -1 0 0 2 0 0 1 0 0 0 0 1