In this case, we need to solve the homogeneous system $Ax = 0$ to find the kernel of $T$. The matrix $A$ is given by
$$ A=\left[\begin{array}{rrr} 1 & -1 & 2 \\ 0 & 1 & 2 \end{array}\right] $$
So, we have the system of equations:
\begin{align*}
x_1 - x_2 + 2x_3 &=
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