试证:如果c1α+c2β+c3γ=0.且c1c3不等于0则l(α,β)=l(β,γ)

Question

试证:如果c1α+c2β+c3γ=0.且c1c3不等于0则l(α,β)=l(β,γ)

Answer 1

由 c1α+c2β+c3γ=0 且c1c3≠0 得
α = -(1/c1)(c2β+c3γ)
γ = -(1/c3)(c1α+c2β)
所以 α,β 与 β ,γ 等价
所以 L(α,β) = L(β ,γ )