ממן11

ממן11 - 11 " 1...

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Unformatted text preview: 11 " 1 : ax + y + z = 4 x + by + z = 3 x + 2by + z = 4 : a 1 1 a 1 1 1 0 0 1 1 b 1 2b 1 4 3 4 : 1 1 b 1 2b 1 b 1 - ab b 4 3 4 1 R1 R a 1 1 1- a 0 3 4 - 3a 1 . (01) : b 0 1 0 0 1 0 0 b 1 - ab b b 1 - ab 1 1 1- a 0 1 1- a 0 3 1 R3 R3 b 4 - 3a 1 3 R1 R1 -bR3 )R 4 - 3a R2 +-1 R2 ( ab 3 1 b b 1 1 1 2b 1 3 4 4 R R - aR 2 1 R32 R3 - R1 , , b = 0 1 0 0 1 0 0 0 0 1 0 1 0 1 1- a 0 1 0 1- a - 2ab + 4b - 1 R2 R3 b 1 b 2 1 b - 2ab + 4b - 1 b 2 , , . 2b - 1 , a = 1 b .b 1 2 1 a = 1 2 : , , b = 1 0 1 2 0 1 0 2 , : . x+z =2 y=2 . P = {(t ,2,2 - t ) | t R} , t = x : a 1 1 0 0 0 1 0 1 0 1- a 2 R3 1 R3 1 1- a b - 2ab + 4b - 1 b 1 0 0 1 0 0 0 1 0 0 1 0 1 0 1 0 0 1 2 1 R1 R3 R1 - b 2ab - 4b + 1 ab - b 2b - 1 ab - b 1 b 2ab - 4b + 1 ab - b . , . a 1, b 0 , . t (t ,2,2 - t ) . a = 1, b = . a = 1, b 1 2 1 b = 0 2 2 : x + 6 y - 18 z = 0 - 4 x + 5 z = 0 - 3 x + 6 y - 13 z = 0 - 2 x - 2 y + z = 0 . (0,0,0) : , , : - 6 - 18 1 1 6 - 18 R +4 R - 4 0 R32 R32 +3 R11 0 24 - 67 5 R4 R4 + 2 R1 R - 3 6 - 13 0 24 - 67 - 2 - 2 1 0 10 - 35 : , .1 - 18 1 6 - 18 5 1 6 R3 - R 0 24 - 67 R3 2 0 24 12 - 67 11 0 10 - 35 0 0 - 62 12 3- 3 , , - , . - , . (0,0,0) , : 2 x - 3 y - 7 z + 5t + 2 w = -2 x - 2 y - 4 z + 3t + w = -2 2 x - 4 z + 2t + w = 3 x - 5 y - 7 z + 6t + 2 w = -7 : 2 - 3 - 7 1 - 2 - 4 2 0 - 4 1 - 5 - 7 1 0 0 0 1 0 0 0 1 0 0 0 2 - 2 1 - 2 1 - 2 R1 R2 2 - 3 2 0 1 3 2 - 7 1 - 5 -2 -4 3 1 - 2 1 R13 R13+ 24R22 0 1 1 -1 0 2 R4 R 4 - 3 R 2 R R + R 0 4 8 - 4 -1 7 -3 -3 3 1 - 5 0 5 3 2 6 0 0 0 1 0 0 0 1 1 1 R 1 R 0 2 3 3 4 0 0 1 0 2 2 0 1 : x + t = 2 y - t = 2 z = 0 w = 1 -4 -7 -4 -7 3 5 2 6 1 - 2 R2 R2 - 2 R1 2 - 2 R34 R34 -2 R1 R - R R1 1 3 2 - 7 1 1 2 R + R -1 0 2 R13 R13- R44 R 0 - 1 - 1 0 1 1 2 2 R12 R12+-2RR3 R R 3 0 1 .2 0 -2 1 1 0 4 0 0 0 0 0 1 0 -2 1 1 1 -1 0 4 0 0 0 0 0 1 0 0 0 1 0 -1 1 0 0 0 0 -2 1 1 1 -1 0 1 0 0 0 0 , - . P = {( 2 - s,2 + s,0, s,1) | s R} , s = t 3 .1 , A , . ad - bc 0 (i) : : a 0 1 a b R1 a R1 1 b R2 R2 -cR1 1 A= a c d c d 0 b R R - b R 1 0 1 1 2 a 1 a 0 1 0 1 b a a R2 -R2 ad bc ad - bc a a 1 - . a 0 - ) ad - bc a (. a 0, ad - bc 0 .- , , b 0 , bc 0 , ad - bc 0 , a = 0 .c 0 d 0 b R1 R2 c d R1 R1 - b R2 c 0 1 0 A= 0 1 c d 0 b 0 b 1 R1 R1 c 1 R2 R2 b .- , . ,- (ii) . ad - bc = 0 : : a 0 1 a b R1 a R1 1 b R2 R2 -cR1 1 A= a c d c d 0 b a = 1 ad - bc 0 a b a 0 , . - . c = 0 b = 0 , bc = 0 , ad - bc = 0 - , a = 0 , , b = 0 . ,- : , c = 0, b 0 d 0 b R2 R2 - b R1 0 b A= 0 0 0 d . , . ad - bc 0 , . ad - bc 0 (ii)- (i) . ad - bc = 0 A 0 : (i) : a 0 c a b R2 R2 - a R1 a A= 0 c d .2 b a b ad - bc = 0 0 a . , b = 0 , bc = 0 , ad - bc = 0 - : a = 0 :c = 0 : : b = 0 0 0 A= c d : , c = 0, b 0 d 0 b R2 R2 - b R1 0 b A= 0 d 0 0 , . . , . ( x 0 , y 0 ) (ii) : a 0 ,(i) ax 0 + by 0 = 0 : ax0 + by 0 = 0 , . (x 0 , y 0 ) , . S = {(x 0 , y 0 ) | R} : b = 0 - , a = 0 ,(i) cx0 + by 0 = 0 . : b 0, a = 0 by 0 = 0 y0 = 0 , , , x0 0 , . , (x 0 ,0) . S = {(x 0 , y 0 ) | R} 4 - 0 , , {u , v, w} . u , v, w : u - v - w, u + v - 2 w, u + w (i) .1 1 (u - v - w) + 2 (u + v - 2 w) + 3 (u + w) = = 1u - 1v - 1 w + 2 u + 2 v - 2 2 w + 3 u + 3 w = = (1 + 2 + 3 )u + ( 2 - 1 )v + (3 - 1 - 22 ) w = : , 1 = 1 + 2 + 3 , 2 = 2 - 1 , 3 = 3 - 1 - 2 2 = 1u + 2 v + 3 w , u , v, w , : . 1 = 2 = 3 = 0 , . 1 + 2 + 3 = 0 2 - 1 = 0 - - 2 = 0 1 2 3 , : 1 1 R R + R 1 1 1 R - R 1 1 2 2 1 - 1 1 0 R3 0 2 1 R32 3 0 R3 R3 + R1 - 1 - 2 1 0 - 1 2 0 1 0 3 1 0 3 R R -3 R 1 1 1 3 R 0 1 - 2 R3 3 0 1 - 2 R12 +3 0 R2 2 R 5 0 0 5 0 0 1 0 1 1 R R -R 1 1 2 1 - 2 R3 R3 - 2 R1 2 1 0 0 1 0 0 1 - , .- , , - 0 , , u - v - w, u + v - 2 w, u + w . , 1 1 (u + 3v - w) - (u + v - 3w) 2 2 .2 (ii) : v+w= , vi + w , , v1 + w, v 2 + w, , v k + w : vi + w = 1 (v1 + w) + + i -1 (vi -1 + w) + i (vi +1 + w) + + k -1 (v k + w) vi + w = 1v1 + + i -1vi -1 + i vi +1 + + k -1v k + (1 + + k -1 ) w (1 - 1 - - k -1 ) w = 1v1 + + i -1vi -1 + vi + i vi +1 + + k -1v k . = 1 - 1 - - k -1 , : = 0 - 0 w = 1v1 + + i -1vi -1 + vi + i vi +1 + + k -1v k 1v1 + + i -1vi -1 + vi + i vi +1 + + k -1v k = 0 , v1 , v 2 v k .1 vi , , 0 - : 0 , w = 1v1 + + i -1vi -1 + vi + i vi +1 + + k -1v k 1 w = 1 v1 + i -1 vi -1 + vi + i vi +1 + + k -1 v k . v1 , v 2 v k w , 5 . x1 a 1 + + x m a m = b . 1 a 1 + + m a m = b , ( 1 , , m ) - x1 a 1 + + x m a m = 0 , . 1 a 1 + + m a m = 0 , , (1 , m ) . ( 1 + 1 )a 1 + + ( m + m )a m = b , x1 a 1 + + x m a m = b ( 1 , , m ) . : (1 , m ) = 0 , . m n , - {a1 , a m } , - {a1 , a m } - . m = n , m n , , R n - n . , , x1 a 1 + + x m a m = c c R n . R n {a1 , , a m } . , R n {a1 , , a m } , m < n {a1 , , a m } , m = n , m n . m n , - , R n n . R n . ( 1 , , m ) , x1 a 1 + + x m a m = b . 1 i m i = i - , ( 1 , , m ) , : , - .3 .2 .1 1 a1 + + m a m = b 1 a 1 + + m a m = b : ( 1 - 1 )a 1 + + ( m - m )a m = 0 , - {a1 , , a m } , . , i = i , i - bi = 0 , 1 i m ...
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