Question

Find two dependence relations among the following 5 vectors in R³: A. u₁ = [ 9 5 1] B.u₂ = [ -6 -3 -1] C. u₃ = [3 2 2] D. u₄ = [-18 -9 -3]

Answer 1

The two dependence relations among the given vectors in R³ are u₂ = -2u₁ + u₃ and u₄ = -2u₂ - 3u₃.

Step-by-step explanation:

The question asks to find two dependence relations among the given vectors in R³. In order to determine dependence, we need to check whether a linear combination of any two vectors results in the other vectors.

1. Dependence relation 1: u₂ = -2u₁ + u₃
2. Dependence relation 2: u₄ = -2u₂ - 3u₃

By expressing each vector in terms of the other vectors, we can see that these dependence relations hold true.