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 \(A\text{?}\)

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