(Solved):   The liner transformation The linear transformation \( T: R^{3} \rightarrow R^{2} \) is def ...

 

The liner transformation

The linear transformation \( T: R^{3} \rightarrow R^{2} \) is defined by \( T(\mathbf{x})=A \mathbf{x} \), where \[ A=\left[\begin{array}{ccc} 0 & -2 & 6 \\ 10 & 0 & 13 \end{array}\right] \] Find \( \operatorname{Ker}(T) \). \[ \begin{array}{l} \{(-13 t, 30 t, 10 t), t \in R\} \\ \{(13 t, 30 t,-10 t), t \in R\} \\ \{(-13 t, 30 t,-10 t), t \in R\} \\ \{(-13,30,10)\} \end{array} \]