x1+2x2+入x3=0--①,2x1+5x2-x3=0---②,x1+x2+13x3=0---③,
由①(-2)+②得x2+(-1-2λ)x3=0---④
由①(-1)+③得-x2+(13-λ)x3=0---⑤
由④+⑤得(12-3λ)x3=0,所以,λ=4时方程组有非零解.
由④得x2=9x3.由①得x1=-22x3,(x3为任意常数).
故
x1=-22x3
x2=9x3
(x3为任意常数).
x1+2x2+入x3=0--①,2x1+5x2-x3=0---②,x1+x2+13x3=0---③,
由①(-2)+②得x2+(-1-2λ)x3=0---④
由①(-1)+③得-x2+(13-λ)x3=0---⑤
由④+⑤得(12-3λ)x3=0,所以,λ=4时方程组有非零解.
由④得x2=9x3.由①得x1=-22x3,(x3为任意常数).
故
x1=-22x3
x2=9x3
(x3为任意常数).