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Linear Algebra: Linear Transformations - Rotations

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Calculate the standard matrix for each of the following linear transformations T.

a. T: R^2 -> R^2 given by rotating -pi/4 counterclockwise about the origin and then reflecting across the line x_1 - x_2 = 0.

b. T: R^3 -> R^3 given by rotating pi/2 counterclockwise about the x_1-axis (as viewed from the positive side) and then reflecting across the plane x_2 = 0.

c. T: R^3 -> R^3 given by rotating -pi/2 counterclockwise about the x_1-axis (as viewed from the positive side) and then rotating pi/2 about the x_3-axis.

Solution Summary

Linear transformations (rotations) are investigated in this solution, which is provided through step by step explanations in a Word document attached.

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Problem (a)
By rotating counterclockwise about the origin, we obtain the matrix

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