增广矩阵的解题顺序， 请大神帮忙做一下这道题，要具体点的步骤，中间最少要写出转化后...
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-2x1+x2+x3 = 0
x1-2x2+x3 = 3
x1+x2-2x3 = -3
解 ： 增广矩阵 (A, b) =
[-2 1 1 0]
[ 1 -2 1 3]
[ 1 1 -2 -3]
初等行变换为
[ 1 -2 1 3]
[ 0 3 -3 -6]
[ 0 -3 3 6]
初等行变换为
[ 1 0 -1 -1]
[ 0 1 -1 -2]
[ 0 0 0 0]
r(A, b) = r(A) = 2 < 3, 方程组有无穷多解。
方程组化为
x1 = -1 + x3
x2 = -2 + x3
取 x3 = 0， 得特解 (-1, -2, 0)^T。
导出组为
x1 = x3
x2 = x3
取 x3 = 1， 得基础解系 (1, 1, 1)^T
方程组通解是 x = k(1, 1, 1)^T + (-1, -2, 0)^T。
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