Define the linear transformation \begin{equation*} \ltdefn{T}{\complex{3}}{\complex{2}},\quad \lt{T}{\colvector{x_1\\x_2\\x_3}}=\colvector{2x_1-x_2+5x_3\\-4x_1+2x_2-10x_3} \end{equation*} Find a basis for the kernel of $T$, $\krn{T}$. Is $T$ injective?