齐次线性方程组:常数项全部为零的线性方程组,及方程组中只有带 ′ x ′ 'x' ′x′ 的项和 ′ 0 ′ '0' ′0′ 项。例如:
{ 2 x 1 + 3 x 2 + 4 x 3 = 0 4 x 1 + 5 x 2 + 6 x 3 = 0 6 x 1 + 7 x 2 + 8 x 3 = 0 left{begin{matrix} &2x_1+3x_2+4x_3=0 \ &4x_1+5x_2+6x_3=0 \ &6x_1+7x_2+8x_3=0 end{matrix}right. ⎩⎨⎧2x1+3x2+4x3=04x1+5x2+6x3=06x1+7x2+8x3=0
相应的,一个非齐次线性方程组例子如下:
{ 2 x 1 + 3 x 2 + 4 x 3 = 4 4 x 1 + 5 x 2 + 6 x 3 = 5 6 x 1 + 7 x 2 + 8 x 3 = 6 left{begin{matrix} &2x_1+3x_2+4x_3=4 \ &4x_1+5x_2+6x_3=5 \ &6x_1+7x_2+8x_3=6 end{matrix}right. ⎩⎨⎧2x1+3x2+4x3=44x1+5x2+6x3=56x1+7x2+8x3=6
参考:
1. 齐次线性方程组 [百度百科]