Question regarding multiple steps in linear mapping

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SUMMARY

The discussion focuses on projecting a point in R2 onto the line defined by the equation x2 = x1 (sqrt(3)) and subsequently rotating it 30 degrees clockwise. The user proposes a 2x2 matrix for the projection as follows: sqrt(3) 0; 0 1, and a rotation matrix defined by cos(x) sin(x); -sin(x) cos(x). The key takeaway is that to combine these transformations, one must multiply the matrices in the correct order.

PREREQUISITES
  • Understanding of linear transformations in R2
  • Familiarity with matrix multiplication
  • Knowledge of rotation matrices
  • Basic trigonometry, specifically sine and cosine functions
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  • Study the properties of linear transformations in R2
  • Learn about matrix multiplication techniques
  • Explore the derivation of rotation matrices
  • Investigate the effects of combining multiple transformations in linear algebra
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Mathematicians, physics students, and anyone interested in linear algebra and transformations in two-dimensional space.

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Hi, I'm having some difficulty with this problem. I need to project a point in R2 to the line x2 = x1 (sqrt(3)) and then rotate it 30 degrees clockwise.

I believe the 2x2 matrix to map it is just

sqrt(3) 0
0 1

and to rotate a vector clockwise as opposed to counter clockwise I think is

cosx sinx
-sinx cosx

I could be wrong about these 2 matrices. Is there anyway to merge the two? Do I multiply them? Thanks.
 
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Yes, you "merge" two matrices by multiplying them. Be sure to multiply in the right order.
 

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