Exercise 3

Suppose that $A$ is a $3\times2$ matrix whose columns are $\vvec_1$ and $\vvec_2$; that is, $$A = \left[\begin{array}{rr} \vvec_1 & \vvec_2 \end{array} \right]$$.

1. What is the dimension of the vectors $\vvec_1$ and $\vvec_2$?

2. What is the product $A\twovec{1}{0}$ in terms of $\vvec_1$ and $\vvec_2$? What is the product $A\twovec{0}{1}$? What is the product $A\twovec{2}{3}$?

3. If we know that $$A\twovec{1}{0} = \threevec{3}{-2}{1},~~~ A\twovec{0}{1} = \threevec{0}{3}{2},$$ what is the matrix $A$?