Determine the matrix that performs a horizontal compression, Mathematics

(a) Determine the matrix that first rotates a two-dimensional vector 180° anticlockwise, and then per- forms a horizontal compression of the resulting vector by a factor 1/2 (leaving the vertical component unchanged).

(b) Determine the matrix that first performs a horizontal compression by a factor 1/2 (leaving the vertical component unchanged) for a two-dimensional vector, and then rotate the resulting vector 180° anticlockwise.

(c) Are the two matrices in (a) and (b) the same? Explain why, or why not.

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