ממן16

ממן16 - 16 " 1...

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Unformatted text preview: 16 " 1 3 0 -4 1 -2 1 :A= 0 -3 2 t -3 0 4 t -1 2 -1 t - 1 det(tI - A) = -1 t - 1 2 = (t - 3) +4 = 0 t +3 -2 0 -2 0 t +3 = (t - 3)(t - 1)(t + 3) + 4(2t - 2) = (t - 1)(t 2 - 1) = (t - 1) 2 (t + 1) . = -1 - = 1 , . 1 - 2 , , : , = 1 - 0 2 0 4 x 1 0 2 y = 0 - 2 0 4 z - 0 , , , , , dim V1 = 2 , 1 . = 1 , X 1 = [ 0 , 1 , 0] , X 2 = [ 2 , 0 , 1] t t .1 . A , = -1 - - 0 4 0 4 x 1 -2 2 y = 0 - - 0 2 0 2 z - , , , dim V-1 = 1 - , 2 , . . , = -1 . A , X 3 = [ 2 , 1 , 2] t , A .VII.21 , A , - " X 1 , X 2 , X 3 ,VII.3 , , A 1 0 0 1 0 B= 0 0 -1 0 ) X 1 , X 2 , X 3 . A - ( = 1, = 1, = -1 , X 1 , X 2 , X 3 ,VII.12 P = [ X1 X 2 X 3 ] 0 2 2 0 1 = 1 1 2 0 . A . A R 3 T , B - A ,' . T B , . T 2001 = , B - , [ T ] B 2001 2001 .2 = B 2001 , 1 12001 0 0 0 1 0 = 0 12001 = 0 0 0 -1 0 0 2001 0 0 0 1 0 1 0 B = 0 = 2001 (-1) 0 -1 0 F Hom(V , W ) t M nt m . T 2001 B - ,-- , T 2001 = T , . . T 2001 ( x, y, z ) = T ( x, y, z ) = (3x - 4 z , x + y - 2 z , 2 x - 3 z ) 2 , R 3 . B = (u1 , u2 , u3 ) = ( (1,1,1), (1,1, 0), (1, -1, 0) ) . R 3 - 3 - . Tu3 = (a - 4, a + 6, 0) : [ Tu3 ] B . [ Tu2 ] B = [ 0, - 5, 0] - [ Tu1 ] B = [ 2, 0, 0] t t , Tu3 = 1u1 + 2 u2 + 3u3 - 1 , 2 , 3 (a - 4, a + 6, 0) = 1 (1,1,1) + 2 (1,1, 0) + 3 (1, -1, 0) = = (1 , 1 , 1 ) + ( 2 , 2 , 0) + ( 3 , - 3 , 0) = = (1 + 2 + 3 , 1 + 2 - 3 , 1 ) R 1 + 2 + 3 = a - 4 1 + 2 - 3 = a + 6 1 = 0 . [ Tu3 ] B = [ 0, a + 1, - 5] , 1 = 0, 2 = a + 1, 3 = -5 t B T A A = [T]B 2 0 0 -5 a + 1 = 0 0 0 -5 . A t-2 0 0 det(tI - A) = 0 t + 5 -a - 1 = (t - 2)(t + 5) 2 0 0 t +5 , = -5 - = 2 A , : . 2 - 1 = 2 : A . A T ,VII.11 0 0 x 0 0 7 - a - 1 y = 0 0 0 0 7 z 0 . 1 , 2 . = 2 : , = -5 - 0 x 0 7 0 0 -a - 1 y = 0 0 0 0 0 z 0 , 1 , , , a = -1 . = -5 , , 2 A VII.21 , A . T , , 2 , , a t -1 A , . : 1 = -5 . T 3 .1 ...
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