Subject: Elementary Linear Algebra (Linear Transformations)
Let T: R^3 → R^2 be the linear transformation for which T([1, –1, 0]) = [2, 1], T([0, 1, –1]) = [–1, 3], and T([0, 1, 0]) = [0, 1].
Find T([–1, 1, 2]).
Give a formula for T([x1, x2, x3]), for any [x1, x2, x3] ∈ R^3.