讨论下列线性方程组的解：
{x1+2x2-3x3+x4=3
{x1+4x2+5x3+2x4=2
{2x1+9x2+8x3+3x4=7
{3x1+7x2+7x3+2x4=12
对增广矩阵进行行初等变换： (1 2 3 1 3 1 4 5 2 2 2 9 8 3 7 3 7 7 2 12) → (1 2 3 1 3 0 2 2 1 -1 0 5 2 1 1 0 1 -2 1 3) → (1 2 3 1 3 0 1 -2 1 3 0 2 2 1 -1 0 5 2 1 1) → (1 2 3 1 3 0 1 -2 -1 3 0 0 6 3 -7 0 0 12 6 14) → (1 2 3 1 3 0 1 -2 1 3 0 0 6 3 -7 0 0 0 0 0) 由此可见原方程组同解于 {x1+2x2+3x3+x4=3 {x2-2x3-x4=3 {6x3+3x4=-7 {x4=x4 故方程组有无穷多组解．
