Undergrad Linear transformation T: R3 -> R2

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To find the linear transformation T: R3 -> R2, the vectors (1,0,-1) and (2,1,3) are used to express (8,3,7) as a linear combination of these vectors. The transformation is defined by T(1,0,-1) = (2,3) and T(2,1,3) = (-1,0). By determining the coefficients for the linear combination, the linearity property of T can be applied to calculate T(8,3,7). The solution involves solving a system of equations to express (8,3,7) in terms of the given vectors. Ultimately, this approach allows for the computation of T(8,3,7) using the defined transformation.
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TL;DR
Linear transformation T: R3 --> R2

Homework Statement

Find the linear transformation [/B]
T: R3 --> R2 such that:

𝑇(1,0,−1) = (2,3)
𝑇(2,1,3) = (−1,0)

Find:

𝑇(8,3,7)
Does any help please?
 
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Express (8,3,7) as a linear combination of the two other vectors in the problem statement and apply linearity of the transformation.
 

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