Worksheet: Linear Transformations in Planes: Projection

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).

  • A1141−23−24−63−69
  • B1161−23−24−63−69
  • C114123−2−4−6369
  • D121−23−24−63−69
  • E12123−2−4−6369

Q2:

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

  • A110123000309
  • B14123000309
  • C16103000309
  • D110103000309
  • E14103000309

Q3:

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

  • A1912351015369
  • B135153525153159
  • C19153525153159
  • D13512351015369
  • E126153525153159

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