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Problem 2. (20 pts.) show that T is a linear transformation by finding a matrix that...

Problem 2. (20 pts.) show that T is a linear transformation by finding a matrix that implements the mapping. Note that x1, x2, ... are not vectors but are entries in vectors. (a) T(x1, x2, x3, x4) = (0, x1 + x2, x2 + x3, x3 + x4) (b) T(x1, x2, x3, x4) = 2x1 + 3x3 − 4x4 (T : R 4 → R)

Problem 3. (20 pts.) Which of the following statements are true about the transformation matrix T found for parts (a) and (b) of problem 2. Justify your answer.

1. T is onto.

2. T is one to one.

3. The set of the column vectors of the transformation matrix of T is linearly independent.

4. Domain and codomain of the transformation is R 4 .

5. This transformation is able to span the entire codomain.

Can someone please solve problem 1 and 2 above. Please include the reasoning behind the answers you got.

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