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negation
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Homework Statement
Say if f is a linear transformation from R2 to R3 with f(1,0) = (1,2,3) and f(0,1) = (0,-1,2).
Determine f(x,y).
The Attempt at a Solution
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 Rn and {t1,t2,t3...tn} is a basis for Rm
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:R2 →R3
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
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