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
左:(a1a2a3+a2a2a3+a13a2a2-a1a2a12-a12a2a23-a13a2a31)x1a13 右=(ba291a3-b2a12a2a43-ba242a13+b2a13a2a1 b,a3302a23-b3 a13a12a23-b,a330a22a13+b3 a13a22a13) 右=(ba2q3+b241242+b2a13a2-ba23a2-b2a12a3-b2a13a2)1 a,aa t aaaa+ aara 可得 13 a21)x1 1221033-13223 b,a2,a2+ +aa b 23432-a1 33 左端项为方程组系数矩阵对应的三阶行列式 1a23+a12al23l31+a13421a32 123432-a12a2143-al1342a31
可得 左端项为方程组系数矩阵对应的三阶行列式 1 23 32 12 2 33 13 22 3 1 22 33 12 23 3 13 32 2 11 23 32 12 21 33 13 22 31 1 11 22 33 12 23 31 13 21 32 ) ( b a a a b a a a b b a a a a b a a b a a a a a a a a a x a a a a a a a a a − − − = + + − − − + + 11 23 32 12 21 33 13 22 31 11 22 33 12 23 31 13 21 32 31 32 33 21 22 23 11 12 13 a a a a a a a a a a a a a a a a a a a a a a a a a a a A − − + + − = = 11 22 33 12 23 31 13 21 32 11 23 32 12 21 33 13 22 31 1 13 左：(a a a + a a a + a a a − a a a − a a a − a a a ) x a ( - ) ( - ) 1 33 12 23 3 13 12 23 1 33 22 13 3 13 22 13 1 23 12 33 2 13 12 33 1 23 32 13 2 13 32 13 b a a a b a a a b a a a b a a a b a a a b a a a b a a a b a a a − + 右 = − + − 1 22 33 3 12 23 2 13 32 1 23 32 2 12 33 3 13 22 13 右 = (b a a + b a a + b a a -b a a -b a a -b a a )a
6, 6, 1a2223+a12423231+a134212 1a2332-12a2143-132221 ba2a3+b2a12a2+b2a13a2-b3a1242-ba23a2-b2a12a3 b2a1(3+b1a31a23+b2a13a21-b2 baa,-6 b2412+b2a3112+b ba2431-b2a321-b 前提:|A|≠0平面(1)(2)(3)的交点
11 23 32 12 21 33 13 22 31 11 22 33 12 23 31 13 21 32 31 32 33 21 22 23 11 12 13 a a a a a a a a a a a a a a a a a a a a a a a a a a a A − − + + − = = A b a a b a a b a a b a a b a a b a a x 1 22 33 3 12 23 2 13 32 3 13 22 1 23 32 2 12 33 1 + + − − − = A b a a b a a b a a b a a b a a b a a x 2 11 33 1 31 23 3 13 21 2 13 31 3 23 11 1 21 33 2 + + − − − = 3 2 1 b b b A b a a b a a b a a b a a b a a b a a x 3 11 22 2 31 12 1 32 21 1 22 31 2 32 11 3 21 12 3 + + − − − = 3 2 1 b b b 3 2 1 b b b ¾ 前提： |A| ≠ 0 平面(1) (2) (3)的交点
三阶行列式展开式的计算 >例如232|=1×3×0+(-20+0 20 (-15)-(-4)-0 1-42 课堂练习 30 245 答案:72
三阶行列式展开式的计算 三阶行列式展开式的计算 ¾ 例如 ( 15 ) ( 4 ) 0 1 1 3 0 ( 20 ) 0 1 2 0 2 3 2 1 0 5 − − − − = − = × × + − + − − − − ? 2 4 5 3 0 3 1 4 2 = − − − ¾ 课堂练习： ¾ 答案： 72
课堂练习2:求解方程23x=0 解D=3x2+4x+18-9x-2x2-12 x2-5x+6 由x2-5x+6=0 x=2或x=3
0 4 9 2 3 1 1 1 2 = x 求解方程 x ¾ 解 3 4 18 9 2 12 2 2 D = x + x + − x − x − 5 6 2 = x − x + 5 6 0 2 由 x − x + = x = 2 或 x = 3 ¾ 课堂练习2：