Let $T({\bf x})=A{\bf x}$ for the matrix $A$ and

$A=\left[\begin{array}{ccc} 2 &1 &-4\cr -5 &4 &-3\cr 7 &1 &-9 \end{array}\right]$, ${\bf b}=\left[\begin{array}{c}1\\2\\1\\\end{array}\right]$, and ${\bf c}=\left[\begin{array}{c}1\\4\\1\\\end{array}\right]$.

Select true or false for each statement.

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

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