Math 260, Spring 2017, Assignment 3
From cartan.math.umb.edu
No doubt many people feel that the inclusion of mathematics among the arts is unwarranted. The strongest objection is that mathematics has no emotional import. Of course this argument discounts the feelings of dislike and revulsion that mathematics induces....
- - Morris Kline, Mathematics in Western Culture
Carefully define the following terms, then give one example and one non-example of each:[edit]
- Rank (of a matrix).
- Sum (of two geometric vectors).
- Scalar multiple (of a geometric vector).
- Linear combination (of a set of geometric vectors).
- Span (of a set of geometric vectors).
- Coordinates (of a geometric vector, with respect to a pair $\vec{e}_1,\vec{e}_2$ spanning the plane, or with respect to a triple $\vec{e}_1,\vec{e}_2,\vec{e}_3$ spanning three-dimensional space).
Solve the following problems:[edit]
- Section 1.3, problems 2, 3, 4, 6, and 8 (compare also 7 from last week's assignment).
- Is it possible to span a plane with a single vector? What is the smallest number of vectors that can be made to span a plane?
- Is it possible to span ordinary three-dimensional space (that is, the space that you live in) with two vectors? What is the smallest number of vectors that can be made to span ordinary space?
