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Find the standard matrix for the following transformation T : R 4 → R 3 :...

Find the standard matrix for the following transformation T : R 4 → R 3 : T(x1, x2, x3, x4) = (x1 − x2 + x3 − 3x4, x1 − x2 + 2x3 + 4x4, 2x1 − 2x2 + x3 + 5x4) (a) Compute T(~e1), T(~e2), T(~e3), and T(~e4). (b) Find an equation in vector form for the set of vectors ~x ∈ R 4 such that T(~x) = (−1, −4, 1). (c) What is the range of T?

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