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How can I use the given linear transformation to determine f(x,y)?
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[QUOTE="negation, post: 4697478, member: 496157"] [h2]Homework Statement [/h2] Say if f is a linear transformation from R[SUP]2[/SUP] to R[SUP]3[/SUP] with f(1,0) = (1,2,3) and f(0,1) = (0,-1,2). Determine f(x,y). [h2]The Attempt at a Solution[/h2] I understand the theorem on linear transformation and bases but unsure as to how I should apply it in practice. Should I be performing the linear transformation test? But the question has already specified that f is a linear transformation. Edit: {u1,u2,u3...un} is a basis for R[SUP]n[/SUP] and {t1,t2,t3...tn} is a basis for R[SUP]m[/SUP] then there is a unique linear transformation such that f maps (u1) to t1: f(u1) = t1 This can be expressed as f(u1) = t1, f(u2) = t2, f(u3) = t3...f(un) = tn f:R[SUP]2[/SUP] →R[SUP]3[/SUP] f(e1) = (1,2,3) ∴f(1,0) = (1,2,3) ∴f(1) = 1, f(0) = 2 f(e2) = (0,-1,2) ∴f(0,1) = (0,-1,2) ∴f(0) = 0, f(1) = -1 [/QUOTE]
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How can I use the given linear transformation to determine f(x,y)?
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