系数行列式 =
λ+3 14 2
-2 λ-8 -1
-2 -3 λ-2
r1+2r2
λ-1 2(λ-1) 0
-2 λ-8 -1
-2 -3 λ-2
c2-2c1
λ-1 0 0
-2 λ-4 -1
-2 1 λ-2
= (λ-1)[(λ-4)(λ-2)+1]
= (λ-1)(λ^2-6λ+9)
= (λ-1)(λ-3)^2.
所以 λ=1 或 λ=3 时方程组有非零解.