入为何值时,线性方程组有唯一解,无解和有无穷多解?当方程组有无穷多解时,线性代数的题!入x1 - x2+x3 =入-3x1 +入x2 + x3 =-2x1 + x2 +入x3 =-2
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增广矩阵 =λ 1 1 λ-3
1 λ 1 -21 1 λ -2r1r31 1 λ -21 λ 1 -2λ 1 1 λ-3
r2-r1,r3-λr1
1 1 λ -20 λ-1 1-λ 0
0 1-λ 1-λ^2 3λ-3
r3+r21 1 λ -20 λ-1 1-λ 0
0 0 2-λ-λ^2 3λ-3
=1 1 λ -20 λ-1 1-λ 0
0 0 (1-λ)(2+λ) 3(λ-1)
当λ≠1且λ≠-2时,r(A)=r(A,b)=3,方程组有唯一解.
当λ=-2时,r(A)=2,r(A,b)=3,方程组无解.
当λ=1时,r(A)=r(A,b)=1