Question: Let \(T:{{R}^{3}}\to {{R}^{3}}\) be a linear transformation. Let \(S=\left\{ {{{\vec{v}}}_{1}},{{{\vec{v}}}_{2}},{{{\vec{v}}}_{3}} \right\}\) be a basis for \({{R}^{3}}\), where

\({{\vec{v}}_{1}}=\left( 0,1,3 \right)\), \({{\vec{v}}_{2}}=\left( -1,1,2 \right)\), \({{\vec{v}}_{3}}=\left( -3,2,2 \right)\)

and

\(T\left( {{{\vec{v}}}_{1}} \right)=\left( 1,1,1 \right)\), \(T\left( {{{\vec{v}}}_{2}} \right)=\left( 1,-1,1 \right)\), \(T\left( {{{\vec{v}}}_{3}} \right)=\left( 1,1,-1 \right)\)

1. Find the formula for \(T\left( {{x}_{1}},{{x}_{2}},{{x}_{3}} \right)\). Use the formula to compute \(T\left( 7,3,-2 \right)\).
2. Find the matrix A that represents T, and use the matrix A to find \(T\left( 7,3,-2 \right)\).

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