Worksheet: Linear Transformations in Planes: Projection

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In this worksheet, we will practice finding the matrix of projection of vectors on a given vector and the image of a vector under a given projection transformation.

Q1:

Find the matrix of the transformation which projects vectors in ℝ onto the vector u=(1,−2,3).

  • A 1 1 4 1 − 2 3 − 2 4 − 6 3 − 6 9
  • B 1 1 6 1 − 2 3 − 2 4 − 6 3 − 6 9
  • C 1 1 4 1 2 3 − 2 − 4 − 6 3 6 9
  • D 1 2 1 − 2 3 − 2 4 − 6 3 − 6 9
  • E 1 2 1 2 3 − 2 − 4 − 6 3 6 9

Q2:

Find the matrix of the transformation which projects vectors in ℝ onto the vector u=(1,0,3).

  • A 1 1 0 1 2 3 0 0 0 3 0 9
  • B 1 4 1 2 3 0 0 0 3 0 9
  • C 1 6 1 0 3 0 0 0 3 0 9
  • D 1 1 0 1 0 3 0 0 0 3 0 9
  • E 1 4 1 0 3 0 0 0 3 0 9

Q3:

Find the matrix of the transformation which projects vectors in ℝ onto the vector u=(1,5,3).

  • A 1 9 1 2 3 5 1 0 1 5 3 6 9
  • B 1 3 5 1 5 3 5 2 5 1 5 3 1 5 9
  • C 1 9 1 5 3 5 2 5 1 5 3 1 5 9
  • D 1 3 5 1 2 3 5 1 0 1 5 3 6 9
  • E 1 2 6 1 5 3 5 2 5 1 5 3 1 5 9

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