Exercise3

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*}
1. What is the dimension of the vectors $$\vvec_1$$ and $$\vvec_2\text{?}$$

2. 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 $$A\twovec{2}{3}\text{?}$$

3. 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 $$A\text{?}$$

in-context