In each of the following, find a formula for the linear transformation on ℝ3 that represents the geometric operation.
(a) Dilation by a factor of 8 followed by counterclockwise rotation about the z-axis by 120°
(b) Projection onto the xz-plane followed by counterclockwise rotation by 45° about the y-axis
(c) Counterclockwise rotation about the z-axis by 120° followed by projection onto the plane 2x + 3y + 4z = 0
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