北京交通大学：《几何与代数》课程教学课件（PPT讲稿）第一章 几何空间中的向量习题课

n1x1+a1x2+n133 222 十 2313 311+ 322 (33 3 12 13 若记 D,=b 22 23 33 11 12 13 或 D 21 22 32

     + + = + + = + + = ; , , 3 1 1 3 2 2 3 3 3 3 2 1 1 2 2 2 2 3 3 2 1 1 1 1 2 2 1 3 3 1 a x a x a x b a x a x a x b a x a x a x b , 3 32 33 2 22 23 1 12 13 1 b a a b a a b a a 若记 D = 31 32 33 21 22 23 11 12 13 a a a a a a a a a 或 D =           1 2 1 b b b

n1x1+a1x2+n133 222 十 2313 311+ 322 (33 3 12 13 记 D,=b 22 23 33 12 13 即 22 235 32 33

 + + = + + = + + = ;,, 3 1 1 3 2 2 3 3 3 3 2 1 1 2 2 2 2 3 3 2 1 1 1 1 2 2 1 3 3 1 a x a x a x b a x a x a x b a x a x a x b, 3 32 33 2 22 23 1 12 13 1 b a a b a a b a a 记 D = , 3 32 33 2 22 23 1 12 13 1 b a a b a a b a a 即 D =

a1x1+a12x2+a13x3=引 a21x1+a2x2+a23x3=b2 ar a a 333 12 13 D=a21 22 23 32 33

     + + = + + = + + = ; , , 3 1 1 3 2 2 3 3 3 3 2 1 1 2 2 2 2 3 3 2 1 1 1 1 2 2 1 3 3 1 a x a x a x b a x a x a x b a x a x a x b 31 32 33 21 22 23 11 12 13 a a a a a a a a a D =

11+a12x2+a13-3 1x1+ 22~2 +aax 311+a32x2+a33 13 得D2=a21b2 23 31 1x1+a12x2+a133 13 21x1+a2x2+a23x3=b2 D=21 22 31Y1+a32x2+ 32

     + + = + + = + + = ; , , 3 1 1 3 2 2 3 3 3 3 2 1 1 2 2 2 2 3 3 2 1 1 1 1 2 2 1 3 3 1 a x a x a x b a x a x a x b a x a x a x b , 31 3 33 21 2 23 11 1 13 2 a b a a b a a b a 得 D =      + + = + + = + + = ; , , 3 1 1 3 2 2 3 3 3 3 2 1 1 2 2 2 2 3 3 2 1 1 1 1 2 2 1 3 3 1 a x a x a x b a x a x a x b a x a x a x b 31 32 33 21 22 23 11 12 13 a a a a a a a a a D =

11+a12x2+a13-3 1x1+ 22~2 +aax 311+a32x2+a33 13 得D2=a21b2 23 31 1x1+a12x2+a133 12 a21x1+a22- 2+23*3=b2= D3=@21 a22 b2 31Y1+a32x2+

     + + = + + = + + = ; , , 3 1 1 3 2 2 3 3 3 3 2 1 1 2 2 2 2 3 3 2 1 1 1 1 2 2 1 3 3 1 a x a x a x b a x a x a x b a x a x a x b , 31 3 33 21 2 23 11 1 13 2 a b a a b a a b a 得 D =      + + = + + = + + = ; , , 3 1 1 3 2 2 3 3 3 3 2 1 1 2 2 2 2 3 3 2 1 1 1 1 2 2 1 3 3 1 a x a x a x b a x a x a x b a x a x a x b . 31 32 3 21 22 2 11 12 1 3 a a b a a b a a b  D =