如何解以下四元一次方程?,请问这个如何解?(2)2X1+X2-X3+X4=13X1-2X2+2X3-3X4=25X1+X2-X3+2X4=-12X1-X2+X3-3X4=4也可能无解.

Question

如何解以下四元一次方程?,请问这个如何解?
(2) 2X1+X2-X3+X4=1
3X1-2X2+2X3-3X4=2
5X1+X2-X3+2X4=-1
2X1-X2+X3-3X4=4
也可能无解.

Answer 1

2 1 -1 1 1 ①
3 -2 2 -3 2 ②
5 1 -1 2 -1 ③
2 -1 1 -3 4 ④
①* -1 + ④,②*-1 +③
2 1 -1 1 1 ①
3 -2 2 -3 2 ②
2 3 -3 5 -3 ③
0 -2 2 -4 3 ④
①* -1 +③
2 1 -1 1 1 ①
3 -2 2 -3 2 ②
0 2 -2 4 -4 ③ => 2X2 -2X3 +4X4 =-4
0 -2 2 -4 3 ④ =>-2X2 +2X3 -4X4 = 3
=>3!=4,-(2X2 -2X3 +4X4) = -2X2 +2X3 -4X4
所以无解