当k=什么时方程组有无穷解
x1 + x2 - x3 = -1;①
① * 2,2x1 + 2x2 - 2x3 = -2;②
① * k,kx1 + kx2 - kx3 = -k;③
2x1 + kx2 - 2x3 = 0;④
kx1 + 2x2 + x3 = k;⑤
④ - ②,( k - 2 )x2 = 2;⑥ k - 2 = 0 时,方程无解;
⑤ - ③,( 2 - k )x2 + ( 1 + k )x3 = 2k;⑦
⑥ + ⑦,( 1 + k )x3 = 2( 1 + k );
1 + k = 0,即 k = -1 时,方程组有无数组解;
k ≠ -1 且 k ≠ 2 时,方程组有唯一解 。
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