The kernel of a linear transformation $T$ is the set of all vectors $x$ such that $T(x) = 0$. In this case, we need to solve the homogeneous system of linear equations $Ax = 0$.
The matrix $A$ is given by
\[ A=\left[\begin{array}{rrr} 1 & -2 & 1 \\ 0 & 2 & 1
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