Exercise 3
Suppose that \(A \) is a \(3\times2\) matrix whose columns are \(\vvec_1\) and \(\vvec_2\text{;}\) that is,
\begin{equation*}
A = \left[\begin{array}{rr} \vvec_1 \amp \vvec_2
\end{array}
\right]\text{.}
\end{equation*}
What is the dimension of the vectors \(\vvec_1\) and \(\vvec_2\text{?}\)
What is the product \(A\twovec{1}{0}\) in terms of \(\vvec_1\) and \(\vvec_2\text{?}\) What is the product \(A\twovec{0}{1}\text{?}\) What is the product \(A\twovec{2}{3}\text{?}\)

Suppose that
\begin{equation*} A\twovec{1}{0} = \threevec{3}{2}{1}, A\twovec{0}{1} = \threevec{0}{3}{2}\text{.} \end{equation*}What is the matrix \(A\text{?}\)