Transcription of 2 鶴亀算 一次連立方程式 消去 ... - cis.twcu.ac.jp
1 (2002 ) 62 , , , . 10 , 28 .. , . , 1800 , . x , y , .x+y=10,(1)2x+4y=28.(2) x y . , . , ..(2) (1) 2 2x+4y=282x+2y=202y=8 x ,y=4 . (1) x+4 = 10, x=6 . , 6 , 4.
2 , , 0 . 1. 4 , 2 , . 1.* a , b ( ) ,a b a 0 ,2a b 4a . , . (2002 ) 7 2. 2x+3y=7,3x+2y=5 .. , .x+y=10,4x+4y=40. x=1,y=9 x= ,y= , . , . , .x+y=10,4x+4y=28. x,y.
3 3. ax+by=0,cx+dy=0 , a,b,c,d , , . , .. , , ( ) .. (2002 ) 83 , .. , , , .. , , .ax+by=ecx+dy=f . d , b adx+bdy=debcx+bdy=bf(ad bc)x=de bfad bc6=0 12 x=ed bfad bc .y , x.
4 Ad bc6=0 ,y=af ecad bc . 4. , . , x,y , . 5.. ,ad bc6=0 , x=ed bfad bc,y=af ecad bc .. , ,ad bc=0 , .. ad bc abcd , .a,b,c,d . , . , . n ,n .126= . (2002 ) 9 , , .(a, b) 1 ,(c, d) 2 . ac 1 , bd 2 .. b 1 2 .. , i j aij.
5 A11a12a21a22 =a11a22 a12a21 . x,y x1,x2 .. , a11x1+a12x2=b1a21x1+a22x2=b2 , . a11a12a21a22 6=0 , x1= b1a12b2a22 a11a12a21a22 ,x2= a11b1a21b2 a11a12a21a22 . ( ). a11a12a21a22 =0 . , : b1a12b2a22 , a11b1a21b2 0 , 0 . 6.
6 (2002 ) 10 . , .1. 1 , 0 1 . 1001 = 1 . a12a11a22a21 = a11a12a21a22 .3. c c .. ca11a12ca21a22 =c a11a12a21a22 , a11ca12a21ca22 =c a11a12a21a22 .4. , . a11+b11a12a21+b21a22 = a11a12a21a22 + b11a12b21a22 , a11a12+b12a21a22+b22 = a11a12a21a22 + a11b12a21b22.
7 , , .5.. a11a21a12a22 = a11a12a21a22 . , .6. 0 . a11a11a21a21 = . a11+ca12a12a21+ca22a22 = a11a12a21a22 , a11a12+ca11a21a22+ca21 = a11a12a21a22 . 7.
