原题
x1 + x2 - x3 = 1 x1 = 1 + x3 - x2
2x1 +3x2 + ax3 = 3
x1 + ax2 + 3x3 = 2
消去 x1 得到
x2 + (a + 2 )x3 = 1 x2 = 1 - (a + 2 )x3
( a -1 )x2 + 4x3 = 1
消去 x2 得到
( 6-a -a^2)x3 = 2 - a
( a-2 )(a + 3) x3 = a - 2
当 a = -3 时, 左侧始终为0, 因此无解
a ≠ 2 且 a ≠ -3 时 有 唯一解
a = 2 时, 有 无穷多解
x2 = 1 - (a + 2 )x3
x1 = 1 + x3 - x2 = ( a + 3 )x3
即
x1 = ( a + 3 )x3
x2 = 1 - (a + 2 )x3
x3 = x3
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