Question: A linear transformation \(T\) is given \((a)\) Find a basis for the range of \(T .(b)\) If the null space of \(T\) is nonzero, find a basis for the null space of \(T\). \(T: R^{4} \rightarrow R^{2}\) defined by

\(T\left(\left[\begin{array}{l}x_{1} \\ x_{2} \\ x_{3} \\ x_{4}\end{array}\right]=\left[\begin{array}{c}x_{2}-2 x_{3} \\ -x_{1}+3 x_{2}+x_{3} \\ x_{1}-4 x_{2}+x_{3} \\ 2 x_{1}-x_{2}+3 x_{3}\end{array}\right]\right.\)

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