###### Exercise4

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 $$T:\real^3\to\real^3\text{.}$$

1. Describe the vectors $$\xvec$$ that satisfy $$T(\xvec) = \zerovec\text{.}$$

2. Describe the vectors $$\xvec$$ that satisfy $$T(\xvec) = \threevec{-8}{9}{2}\text{.}$$

3. Describe the vectors $$\xvec$$ that satisfy $$T(\xvec) = \threevec{-8}{2}{-4}\text{.}$$

in-context