 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2024/paper-2/1/b/solution

(α, β + γ, γ)^{T} = (0, 0, 0)^{T} .

The third component first forces

γ = 0

β = 0

, and the first gives

α = 0

. Thus

α = β = γ = 0 .

Equivalently, the nonzero scalar triple product proves that these three vectors are linearly independent.

 New to topics? Read the docs here!