Worksheet: Projection Matrix

Practice

In this worksheet, we will practice expressing a projection onto a line as a matrix–vector product and finding the projection transformation matrix of a vector.

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 2 1 − 2 3 − 2 4 − 6 3 − 6 9
  • C 1 2 1 2 3 − 2 − 4 − 6 3 6 9
  • D 1 1 4 1 − 2 3 − 2 4 − 6 3 − 6 9
  • E 1 1 6 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 0 3 0 0 0 3 0 9
  • C 1 4 1 2 3 0 0 0 3 0 9
  • D 1 1 0 1 0 3 0 0 0 3 0 9
  • E 1 6 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 3 5 1 2 3 5 1 0 1 5 3 6 9
  • B 1 9 1 5 3 5 2 5 1 5 3 1 5 9
  • C 1 9 1 2 3 5 1 0 1 5 3 6 9
  • D 1 3 5 1 5 3 5 2 5 1 5 3 1 5 9
  • E 1 2 6 1 5 3 5 2 5 1 5 3 1 5 9

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