Question

Find two dependence relations among the following 5 vectors in ℝ³:

u₁ = [-4, -1, -3],
u₂ = [-4, -1, -2].

Answer 1

The dependence relations among the vectors u₁ and u₂ in ℝ³ are u₂ = -1.5u₁.

Step-by-step explanation:

In order to find the dependence relations among the vectors u₁ = [-4, -1, -3] and u₂ = [-4, -1, -2] in ℝ³, we can compare their components.

Let's take the ratio between the components of the two vectors:

-4/-4 = 1
-1/-1 = 1
-3/-2 = 1.5

All the ratios are equal to 1, except for the last component which is 1.5. Therefore, we can conclude that the dependence relations among the vectors are:

u₂ = -1.5u₁