申論題

4.(15%)下面的問題共有三個子題,只要寫出每個子題的答案即可(不需寫出計算過程),例如: (a) β=1,γ=2。 Let a₁ = [1 0 1 α]^T,a2=[I β 2 2]^T, and a3 = [-2 3 γ -4]^T be three vectors in R⁴, where a, β, and γ are three real parameters, and denote A := [a₁ a₂ a₃] .

(a) (4%) Suppose a is not a positive integer. Find real β and γsuch that{a₁, a₂, a₃} is a linearly dependent set.