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REFLECTION

REFLECTION. REFLECTION. Find a matrix M such that M =. The reflection of through y = mx. v. v. v. v. w. w. The reflection of through. Reflection is a linear transformation. . sin = m. m. . 1. cos = 1. y = mx. .

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REFLECTION

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  1. REFLECTION REFLECTION

  2. Find a matrixM such that M = The reflection of through y = mx v v v v w w The reflection of through Reflection is a linear transformation

  3. sin = m m  1 cos = 1 y = mx 

  4. M = the counterclockwise rotation of through 2 degrees   sin = m  cos = 1 The first column of M  

  5. M = the clockwise rotation of through 2( 90 - )degrees   sin = m  cos = 1 The second column of M 90- 90-

  6. For y = 2x ,

  7. y = 2x

  8. The process of finding a matrix to REFLECT a vector through the line y = mx can be greatly simplified by choosing a different basis y = mx

  9. Choose a different basis: { , } y = mx

  10. T = 1 + 0 T = 0 + -1 The matrix relative to the basis { , } is y = mx

  11. The matrix relative to the basis { , } is

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