增廣矩陣 =
1 -5 2 -3 11
5 3 6 -1 -1
2 4 2 1 -6
r2-5r1,r3-2r1
1 -5 2 -3 11
0 28 -4 14 -56
0 14 -2 7 -28
r2-2r3,r3*(1/14)
1 -5 2 -3 11
0 0 0 0 0
0 1 -1/7 1/2 -2
r1+5r3
1 0 9/7 -1/2 1
0 0 0 0 0
0 1 -1/7 1/2 -2
所以通解為:(1,-2,0,0)'+c1(-9,1,7,0)'+c2(1,-1,0,2),c1,c2 為任意常數(shù).初等變換玩后。怎么就得出這個結果啦？這是解線性方程組的基本方法, 說起來比較麻煩109/7 -1/2 100 00001 -1/71/2-2對應方程組:x1 = - 9/7x3 +1/2x4 +1x2 = 1/7x3 -1/2x4-2(x3,x4) = (0,0) 得特解 (1,-2,0,0)'.(x3,x4) = (7,0) ,(0,2) 得基礎解系 (-9,1,7,0)',(1,-1,0,2)做多了就能直接看出結果來了 ^_^