Mathematics — first biennium · Lesson
In the plane two non-zero vectors are dependent when one is a scalar multiple of the other. Equivalently, the determinant of their components is zero.
Prerequisites: Linear combinations
Goal: Recognize when two plane vectors are scalar multiples and connect dependence with a zero determinant.
In this lesson: Recognize when two plane vectors are scalar multiples and connect dependence with a zero determinant.
New concept: Two plane vectors are linearly dependent when one is a scalar multiple of the other: they have the same direction, possibly opposite orientation. If neither is a multiple of the other, they are linearly independent.
How to proceed: One component ratio is not enough: the factor must be the same in both directions. The determinant provides one combined check.
You can already assume: Linear combinations.
The arrows lie on the same direction: one is a scalar multiple of the other.
Completed exercises: 0/5 · Correct on first attempt: 0
One component ratio is not enough: the factor must be the same in both directions. The determinant provides one combined check.
Data / situation: u=(4,0), v=(-12,0).
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