判断是否有解若有求通解,X1+4X2-3X3+5X4=-23X1-2X2+X3-3X4=42X1+X2-X3+X4=1

Question

判断是否有解 若有求通解,X1+4X2-3X3+5X4=-2 3X1-2X2+X3-3X4=4 2X1+X2-X3+X4=1

Answer 1

增广矩阵 =
1 4 -3 5 -2
3 -2 1 -3 4
2 1 -1 1 1
r1-3r3,r2+r3,r3*(-1)
-5 1 0 2 -5
5 -1 0 -2 5
-2 -1 1 -1 -1
r2+r1,r3+r1
-5 1 0 2 -5
0 0 0 0 0
-7 0 1 1 -6
方程组有解,通解为 (0,-5,-6,0)^T+c1(1,5,7,0)^T+c2(0,2,1,-1)^T.