- #1
PcumP_Ravenclaw
- 106
- 4
Homework Statement
Suppose that ## u = s_1i + s_2j ## and ## v = t_1i + t_2j ##, where s1, s2, t1 and t2 are real
numbers. Find a necessary and sufficient condition on these real numbers
such that every vector in the plane of i and j can be expressed as a linear
combination of the vectors u and v.
Homework Equations
We shall need to consider directed line segments, and we denote the directed
line segment from the point a to the point b by [a, b]. Specifically, [a, b] is the
set of points {a + t(b − a) : 0 ≤ t ≤ 1},
The Attempt at a Solution
As attached.