Activity2.2.3

In addition, Sage can find the product of a matrix and vector using the * operator. For example,

  1. Use Sage to evaluate the product ItemĀ a yet again.

  2. In Sage, define the matrix and vectors

    \begin{equation*} A = \left[ \begin{array}{rrr} -2 \amp 0 \\ 3 \amp 1 \\ 4 \amp 2 \\ \end{array} \right], \zerovec = \left[ \begin{array}{r} 0 \\ 0 \end{array} \right], \vvec = \left[ \begin{array}{r} -2 \\ 3 \end{array} \right], \wvec = \left[ \begin{array}{r} 1 \\ 2 \end{array} \right] \text{.} \end{equation*}

  3. What do you find when you evaluate \(A\zerovec\text{?}\)

  4. What do you find when you evaluate \(A(3\vvec)\) and \(3(A\vvec)\) and compare your results?

  5. What do you find when you evaluate \(A(\vvec+\wvec)\) and \(A\vvec + A\wvec\) and compare your results?

  6. If \(I=\left[\begin{array}{rrr} 1 \amp 0 \amp 0 \\ 0 \amp 1 \amp 0 \\ 0 \amp 0 \amp 1 \\ \end{array}\right]\) is the \(3\times3\) identity matrix, what is the product \(IA\text{?}\)

in-context