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Given the linear transformation T with T(x1, x2) = (3x1 - 2x2, x1 + 4x2, x2), find its standard matrix, that is the unique matrix A with the property that T(x) = Ax for all x. (Note that x1, x2 are entries of x.) Let T: R2 R3 be a linear transformation with T (x1, x2) = (2x1 - x2, -3x1 + x2, 2x1 - 3x2). Is (0, -1, -4) in range of T? If yes, find an x such that T(x) = (0, -1, -4).

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