试用三元一次方程组的解法解四元一次方程组X+Y+Z+U=4,X+Y-Z-U=-2,X-Y+Z-U=0,X+Y-Z+U=2

问题描述:

试用三元一次方程组的解法解四元一次方程组X+Y+Z+U=4,X+Y-Z-U=-2,X-Y+Z-U=0,X+Y-Z+U=2

X+Y+Z+U=4,①
X+Y-Z-U=-2,②
X-Y+Z-U=0,③
X+Y-Z+U=2④
[①+②]/2,X+Y=1,
[①+③]/2,X+Z=2,
[①-④]/2,Z=1.
容易得到X=1,Y=0,U=2.
∴{U=2,
{x=1,
{y=0,
{z=1,.