a1x talc b2(2) 少解三元线性方程组{41+a2x2+03b305) 11+a32x2+n2 消去x3,a23×(1)-a13×(2),得平面(1)(2)的交线 (a1a23-a21a13)x1+(a12a23 )x2=ba23-b2a13(4) 消去x,a33×(1)-a13×(3),得平面(1)(3)的交线 (a143-a3413)x1+(a12a3-a2413)x2=ba3-b2413(5) 同样步骤,(4、5)消去x2 (a1a23-a21a13)(a12a3-a3213)x1-(a1a3-a313)(a12a23-a213)x1 =(ba23-b2a13)(a12a3-a2a13)-(b1a3-b2413)a12a23-a2a13) 左 33 11312033 a122a2C12+a2112a 13 a 32013 (a1aya12423-a343a12a2y-a1a342413+a1414241)x解三元线性方程组 消去x3， a23×(1)- a13 ×(2)，得 消去x3， a33×(1)- a13 ×(3)，得 同样步骤，(4、5)消去x2 ⎪⎩ ⎪⎨⎧ + + = + + = + + = (3) (2) (1) 31 1 32 2 33 3 3 21 1 22 2 23 3 2 11 1 12 2 13 3 1 a x a x a x b a x a x a x b a x a x a x b ( ) ( ) - (4) 11 23 21 13 1 12 23 22 13 2 b1a23 b2a13 a a − a a x + a a − a a x = ( ) ( ) - (5) 11 33 31 13 1 12 33 32 13 2 b1a33 b3a13 a a − a a x + a a − a a x = ( )( ) ( )( ) ( ) ( ) ( )( ) 1 23 2 13 12 33 32 13 1 33 3 13 12 23 22 13 11 23 21 13 12 33 32 13 1 11 33 31 13 12 23 22 13 1 b a b a a a a a b a b a a a a a a a a a a a a a x a a a a a a a a x = − − − − − − − − − − 11 33 12 23 31 13 12 23 11 33 22 13 31 13 22 13 1 11 23 12 33 21 13 12 33 11 23 32 13 21 13 32 13 1 ( ) ( ) a a a a a a a a a a a a a a a a x a a a a a a a a a a a a a a a a x − − − + 左： − − + 平面(1) (2)的交线 平面(1) (3)的交线