Homework #1
Calculate problems #1 and #2 manually and use
http://www.continuummechanics.org/interactivecalcs.html to doublecheck.
 Calculate the length of each vector and find the angle between them:
\({\bf a} = (12, 3, 4)\) and \({\bf b} = (16, 48, 12)\).

Find the area of a triangle whose edges are the two vectors in #1 above.
Ignore units.
Don't do the remaining ones manually. It's too tedious. Just use the above webpage (or Matlab, etc) and write out the results.

Given \(
\quad {\bf A} = \left[
\matrix {
2 & 5 & 1 \\
4 & 8 & 2 \\
6 & 2 & 4 }
\right] \quad
\)
and
\(
\quad {\bf B} =
\left[ \matrix {
3 & 4 & 2 \\
1 & 7 & 5 \\
3 & 2 & 4 }
\right] \quad
\)
Demonstrate that \({\bf A} \cdot {\bf B} \ne {\bf B} \cdot {\bf A}\), but
\( ( {\bf A} \cdot {\bf B} )^T = {\bf B}^T \cdot {\bf A}^T \).

Calculate the double dot product of the two matrices, \({\bf A} : {\bf B}\).

Calculate the inverse of \({\bf A}\) in #3 and confirm that
\({\bf A} \cdot {\bf A}^{1} \; = \; {\bf A}^{1} \cdot {\bf A} \; = \; {\bf I}\).