Question: 3. (6 points) Let T: R3 > R2 be a linear transformation that maps (1,1, 1),(0,1, 0) and (0, 1, 1) to (0, 1), (1,

3. (6 points) Let T: R3 > R2 be a linear transformation that maps (1,1, 1),(0,1, 0) and (0, 1, 1) to (0, 1), (1, 1) and (1, 1), respectively. DO NOT USE elementary algebra. (A) Determine whether T is a matrix transformation or not. Explain why or why not. (solution) (B) If the answer to (A) is 'YES', then find the standard matrix for T. If not, skip this question. (solution) (C) Find the image of (x, y, 2) under the transformation. (solution) (D) Use the definition of Linear Transformation to prove that T is linear. (solution) (E) Find all the preimage(s) of (1,4) under the transformation if there is any. If not, explain why not. (solution) (F) Determine if T is one-to-one or not. Explain why or why not. (solution) (G) Determine if T is onto or not. Explain why or why not. (solution)

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