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Matrix Transformation: Understanding and Solving with Examples

Explore transformation matrices easily using step-by-step solutions with examples for better comprehension and learning.

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Matrix Transformation: Understanding and Solving with Examples

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  1. to to to x1 y1 z1 x2 y2 z2 x3 y3 z3 0 1 0 0 0 1 1 0 0 Direction Cosine Question : If a certain transformation matrix M transforms Then, what is matrix M?

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

  3. to to to x1 y1 z1 x2 y2 z2 x3 y3 z3 0 1 0 0 0 1 1 0 0 x1 x2 x3 y1 y2 y3 z1 z2 z3 M = Remember If M transforms Then :

  4. 0 0 1 1 0 0 0 1 0 cos(a) sin(a) 0 -sin(a) cos(a) 0 0 0 1 to to to cos(a) - sin(a) 0 sin(a) cos(a) 0 0 0 1 RZ(a) = Question : What is the transformation matrix for RZ(a) ? Solution : If RZ(a) transforms Then,

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

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