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Matrix for 30-Degree Counterclockwise Rotation Linear Mapping

Calculate rotation matrix for Rx, a 30-degree counterclockwise rotation of x. Generalize the effect of rotation on each basis vector. Obtain a matrix relative to the standard basis.

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Matrix for 30-Degree Counterclockwise Rotation Linear Mapping

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  1. ROTATION ROTATION ROTATION ROTATION ROTATION Pamela Leutwyler

  2. problem: Rx = the counterclockwise rotation of x through 30 degrees. Find a matrix for the linear mapping R.

  3. Rotate conterclockwise through 30 degrees: Rotate conterclockwise through 30 degrees: First column To find a matrix for a linear mapping relative to the standard basis, We must observe the effect of the mapping on each basis vector: Second column

  4. = = the 30 degree rotation of

  5. This can be generalized: = the  degree rotation of

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