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For the matrix F(\u03b1) = \u005bcos \u03b1 \u2212sin \u03b1 0; sin \u03b1 cos \u03b1 0; 0 0 1\u005d, the product F(\u03b1)F(\u03b2) is equal to

1. F(\u03b1\u03b2)
2. F(\u03b1/\u03b2)
3. F(\u03b1 + \u03b2)
4. F(\u03b1 - \u03b2)

Correct answer: F(\u03b1/\u03b2)

Solution

The product F(α)F(β) represents the composition of two rotations, and the resulting transformation corresponds to the rotation by the angle α/β, which is why the correct option is F(α/β). This reflects the property of matrix multiplication in the context of rotation matrices.

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