Let $A=\left[\begin{matrix} 1 & 1 & 2 \cr -2 & 2 & -12 \cr \end{matrix}\right]$, ${\bf b}=\left[\begin{matrix} -8 \cr 4 \cr 2 \cr \end{matrix}\right]$, and ${\bf c}=\left[\begin{matrix} 2 \cr 4 \cr \end{matrix}\right]$. Define $T({\bf x})=A{\bf x}$.

Select true or false for each statement.

True False  1. The vector ${\bf c}$ is in the range of $T$

True False  2. The vector ${\bf b}$ is in the kernel of $T$