Algebra I: A Basic Course in Abstract Algebra

10.12 Exercise

1. If then
   1. Compute u + v,2u − v,−2u + 1/2v
   2. Display the vectors computed in (i) using arrows on a x−y plane
2. A boat is traveling east across a river at the rate of 6kms/hour while the river's current is flowing south at a rate of 2km/hour.
   1. Find the resultant velocity of the boat.
   2. If the speed of the boat is halved, then what is the resultant velocity of the boat?
3. Using the figure write the following vectors as a linear combination of u and v
   1. a, b, c, d
   2. z, y, z
   3. Is every vector in ℝ² a linear combination of u and v?
   4. Display the vectors 2u − 3v,−3u − 4u
4. Write the system of equations that is equivalent to the given vector equation