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Algebra Level 4

Consider a Euclidean space Rn\mathbb R^{n} and the 3 equations y1=x13+x21,y2=x13,y3=x1+x2+2.\begin{array}{c}&y_{1}=x_{1}^{3}+x_{2}-1, &y_{2}=x_{1}^{3}, &y_{3}=x_{1}+x_{2}+2.\end{array} Now, a transformation T:R2R3T:\mathbb R^{2}\mapsto \mathbb R^{3} is defined by : T(x1,x2)=(x13+x21,x1+x2,x1+x2+2).T\left ( x_{1},x_{2} \right )=\left (x_{1}^{3}+x_{2}-1,x_{1}+x_{2}, x_{1}+x_{2}+2 \right ). Find T(2,8)T\left (2,8 \right ).

Submit your answer as y1+y2y3y_{1}+y_{2}-y_{3}.

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