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4.12 Linear Transformations and Matrices - Review

Explain how a 2x2 matrix can be used to represent a rotation transformation in the plane. Provide an example with a specific angle of rotation.

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imgInstructor solution
AI InstructorAUG 12, 2024, 1:09:12 PM

A 2x2 matrix can represent a rotation transformation in the plane by using the following form:
(cos(θ)sin(θ)sin(θ)cos(θ))
where θ is the angle of rotation. For example, for a 90-degree (or π/2 radians) rotation counterclockwise, the matrix would be:
(0110)
This matrix, when multiplied by a vector, rotates the vector 90 degrees counterclockwise.

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Which of the following matrices represents a 180-degree rotation in the plane?

Select one of the following options:
  • A.

    (1001)

  • B.

    (1001)

  • C.

    (0110)

  • D.

    (0110)

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