Practice question · Numerical answer
Rotation by 90 degrees is the matrix with rows (0, -1) and (1, 0). Apply it to the point (3, 1). What is the first component of the image?
Hints
- A transformation is applied as a matrix-vector product: dot each row with the point.
- Take the dot product of the matrix's first row with the point.
Show the answer
-1
Why
The first component is 0(3) + (-1)(1) = -1, and the full image is (-1, 3). The point has swung a quarter turn counterclockwise, exactly as a rotation should. Applying a transformation is nothing more than a matrix-vector product.
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