(See Solution) Find a generating set for the null space of each linear transformation T. Use your answer to determine whether T is one-to-one. Given: ltext
Question: Find a generating set for the null space of each linear transformation T. Use your answer to determine whether \(T\) is one-to-one.
Given:
\[\begin{array}{l}\text { T: } R^{2} \rightarrow R^{3} \text { defined by } T\left(\left[\begin{array}{l}x_{1} \\ x_{2}\end{array}\right]\right)=\left[\begin{array}{c}x_{1}+x_{2} \\ 0 \\ 2 x_{1}-x_{2}\end{array}\right]\end{array}\]
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