In each of the following, find a formula for the linear transformation on ℝ3 that represen...

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 6

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(b) Dilation by a factor of

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(c) Counterclockwise rotation about the z-axis by 60°

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(d) Clockwise rotation about the z-axis by 45°

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(e) Coordinate rescaling by 4 in the x-direction, 2 in the y-direction, and in the z-direction

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(f) Clockwise rotation by 30° about the y-axis