Exercise 45

  1. Draw the vectors \(\mathbf{a} = \langle 3, 2 \rangle, \mathbf{b} = \langle 2, -1 \rangle,\) and \(\mathbf{c} = \langle 7, 1 \rangle\).
  2. Show, by means of a sketch, that there are scalars s and t such that \(\mathbf{c} = s\mathbf{a} + t\mathbf{b}\).
  3. Use the sketch to estimate the values of s and t.
  4. Find the exact values of s and t.