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] .

(b) (5%) Now let a = 2, β = -1,γ = -5, and let x be a nonzero vector in the null space N(A) of A. Find the value of k to satisty ||x|| ₁ + 2||x||∞ + k||x||₂ = 0.