Question

一道线性代数题x1+λx2+2x3=1 x1+(2λ-1)x2+3x3=1 x1+λx2+(λ+3)=2λ-1 λ取何值时有解 并求出相应的解

写整齐一点x1+λx2+2x3=1
x1+(2λ-1)x2+3x3=1
x1+λx2+(λ+3)=2λ-1
用初等变换做

Answer 1

1 λ 2 1

1 2λ-1 3 1

1 λ λ+3 2λ-1

二三行减第一行
1 λ 2 1

0 λ-1 1 0

0 0 λ+1 2λ-2

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λ+1=0 2λ-2=0 有无穷解 不可能
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λ+1≠0 有唯一解
x3=(2λ-2)/(λ+1)
x2=-x3/(λ-1)
x1=1-2x3-λx2
x=(x1,x2,x3)
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