Question: Consider the linear transformation that projects a 3-vector (x, y, z) onto the xy-plane. (a) If the input vector is (Xins Yins Zin), what

Consider the linear transformation that projects a 3-vector (x, y, z) onto

Consider the linear transformation that projects a 3-vector (x, y, z) onto the xy-plane. (a) If the input vector is (Xins Yins Zin), what is the output vector? (b) Write down a matrix that corresponds to this linear transformation. (c) Geometrically, what happens if we apply this linear transformation twice? How does the final output vector relate to the original input vector? (d) Express your answer to part (c) in terms of matrices and matrix multiplication.

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