Linear Algebra Example Problems – Linear Transformations: Rotation and Reflection

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A linear transformation T: R2 to R2 is examined in this video. For this type of transformation, both the input vectors and output vectors are length 2 and can be easily plotted/visualized in a 2-D coordinate plane.

We find the matrix representation of a linear transformation that rotates points clockwise about the origin by pi/6 radians and then reflects the point through the line x1 = -x2. We also visualize the output of this transformation when the input is the vector x = [1; 0].

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