Exercise 4
Suppose that the matrix
\begin{equation*}
A = \left[\begin{array}{rrr}
1 \amp 3 \amp 1 \\
-2 \amp 1 \amp 5 \\
0 \amp 2 \amp 2 \\
\end{array}\right]
\end{equation*}
defines the matrix transformation \(T:\real^3\to\real^3\text{.}\)
Describe the vectors \(\xvec\) that satisfy \(T(\xvec) = \zerovec\text{.}\)
Describe the vectors \(\xvec\) that satisfy \(T(\xvec) = \threevec{-8}{9}{2}\text{.}\)
Describe the vectors \(\xvec\) that satisfy \(T(\xvec) = \threevec{-8}{2}{-4}\text{.}\)