已知3阶行列式|α,β,γ|=3,求|3α-β+2γ,-α+β+γ,2α+5β-7γ|

Question

已知3阶行列式|α,β,γ|=3,求|3α-β+2γ,-α+β+γ,2α+5β-7γ|

Answer 1

(3α-β+2γ,-α+β+γ,2α+5β-7γ) = (α,β,γ)K
K =
3 -1 2
-1 1 5
2 1 -7
等式两边取行列式
|3α-β+2γ,-α+β+γ,2α+5β-7γ| = |α,β,γ| |K| = 3 * (-45) = -135.