ממן13

ממן13 - 13 " 1 -2i...

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Unformatted text preview: 13 " 1 -2i . -2i = (0, -2) = (2, 3 ) - , -2i = 2 2 . -2i = 2 ( cos 3 + i sin 3 ) 2 2 , z = r (cos + i sin ) . z 4 = -2i 4 = 3 + 2k - r = 4 2 , r 4 ( cos 4 + i sin 4 ) = 2 ( cos 3 + i sin 3 ) 2 2 2 3 : , . = 8 + 3 3 z0 = 4 2 ( cos 8 + i sin 8 ) .1 k (3 + 4k ) = , k = 0,1, 2,3 2 8 z1 = 4 2 ( cos 7 + i sin 7 ) 8 8 z2 = 4 2 ( cos 11 + i sin 11 ) 8 8 z3 = 4 2 ( cos 15 + i sin 15 ) 8 8 .2 , n , c11 - 1 , det C = c11 , . C = , C = [ c11 ] , n =` . det A = det A . det C = det C , det C = c11 - , n = k B .[" B ] det B = det B . n = k + 1 ai j , n = k + 1 A det A . A , : i - .1 det A = -1) ( j =1 n i+ j i j a M A ij = -1)i + j i j iAj ( a M j =1 n . (-1)i + j = (-1)i + j , (-1)i + j . j - i - A Ai j , , k Ai j , k + 1 A - det( Ai j ) = M iAj - , det( Ai j ) = M iAj . det( Ai j ) = det( Ai j ) , : . M iAj = M iAj , det A = -1)i + j i j iAj = -1)i + j i j iAj = ( a M ( a M j =1 j =1 n n z z : , ( z1 2 ) = z1 2 = (-1)i + j i j iAj = a M j =1 n , ( z1 + z2 ) = z1 + z2 , = (-1)i + j i j iAj a M j =1 n : i - A det A = (-1)i + j i j iAj a M j =1 n . , , det A = det A , . det A A = det ( I ) = 1 , At A = I . A t ( ) .2 det , det A = det A . det A ( A ) = 1 , t t ( ) 2 ( ) ( ) det , det A = det ( A ) ,' . det A ( A ) = 1 , zz = z det det . det ( A ) ( A ) = 1 det ( A ) ( A ) = 1 ( ) ( ) , . det ( A ) = 1 , det ( A ) 2 = 1 . , det ( A ) = 1 i - 0 0 i 0 0 i 0 -i 0 A = 0 0 , A = 0 i 0 -i 0 0 t 1 0 0 1 0 I 0 = , . A A = - 0 1 0 t 3 . A = (-i ) = i , 3 2 , R R 2 - , R : R - , . (a, b) z R 2 , ( + )(a, b) = ( ( + ) a, b ) , (a, b) + (a, b) = ( a, b) + ( a, b) = ( a + a, b + b) = ( ( + )a, 2b ) , ( ( + ) a, b ) = ( ( + )a + 2b ) , (a, b) = (3,5) . 5 2 10 - ( ( + )3,5 ) = ( ( + )3 + 10 ) .1 : Q( 2) . = a + 2b, = c + 2d , = s + 2t - , , , , + Q( 2) .2 Q( 2) , + = a + 2b + c + 2d = ( a + c) + 2(b + d ) : . Q( 2) - : , . Q( 2) 2 R , R - , 0 = 0 + 2 Q( 2) : 0 . + 0 = a + 2b + 0 = a + 2b = : Q( 2) - : , + (- ) = 0 , - = -(a + 2b) = - a - 2b Q( 2) . R - , = (a + 2b)(c + 2d ) = (ac + 2bd ) + 2( ad + bc ) Q( 2) : . Q( 2) - : , .- , R - , Q( 2) - 1 = 1 + 2 Q( 2) : 0 . = (a + 2b) = a + 2b = 1 1 : Q( 2) - : , -1 = (a + 2b) -1 = 1 a + 2b a - 2b a b = 2 - 2 2 Q( 2) 2 2 2 2 a - 2b a - 2b a - 2b .- -1 = 1 , , Q( 2) - : . Q( 2) 2 R = 3 .1 R . R M 22 2 , .1 , A = 0 U , , U z R :- U z M 2z 2 1 , 2 . AC = 0, BC = 0 , A, B z U . C : . 1 ( AC ) = 0, 2 ( BC ) = 0 : , M 22 2 - . 1 ( AC ) + 2 ( BC ) = 0 R , , (1 A)C + (2 B)C = 0 . 1 A + 2 B U , (1 A + 2 B )C = 0 R .- U z M 2z 2 , A, B . 2x - y + t = 0 , ( x, y, z , t ) z W x - 3 y + z - 2t = 0 .2 . 2 1 -1 0 1 0 2 5 1 , . 1 - 1 1: 1 0 5 -3 1 -2 . x = 2 5 z - t , y = - 1 5 z - t , x - 2 5 z + t = 0, y - 1 5 z + t = 0 , ( 2 5 a - b, - 1 5 a - b, a, b) R 4 - W , . a, b z R - : - W . R R 4 . (0, 0, 0, 0) z W , , W z , ( 2 5 a - b, - 1 5 a - b, a, b) W , ( 2 5 a - b, - 1 5 a - b, a, b) = ( 2 5 a - b, - 1 5 a - b, a, b) W . , . a, b R . ( 2 5 c - d , - 1 5 c - d , c, d ) , ( 2 5 a - b, - 1 5 a - b, a, b) + ( 2 5 c - d , - 1 5 c - d , c, d ) = = ( 2 5 (a + c ) - (b + d ), - 1 5 ( a + c) - (b + d ), a + c, b + d ) W R - W , . . a + c, b + d . R 4 R R - T z M nz n . R M nz n .3 : ( n z 3 ) n z n , T z ( 0 ) : T - .( 0 ) . A, B ai j , bi j , A, B z T i1 = 2 a i =1 n a a i3 , . i1 = 2 i =1 i =1 n n n a i =1 n n i3 , A T , ai1 = 2 i =1 a i =1 i3 . a b b , i1 + i1 = 2 ai 3 + 2 bi 3 : . i1 = 2 i =1 i =1 i =1 i =1 i =1 n n n n n n b i =1 n n i3 a . A + B T , i1 + bi1 = 2 ai 3 + bi 3 i =1 i =1 R , R M nz n - T , . . a 11 : . AC = 0 . A = a 21 a 11 .A= a 21 2a11 - a12 = 0 2a11 a 11 , . 2a - a = 0 , , 2a21 a 21 21 22 a12 U a22 a12 2 0 = -1 0 0 a22 .2 a 11 , 1 = a11 , 2 = a21 a 21 2a11 2 0 1 0 = + 1 0 2 2 2a21 0 1 2 0 1 0 , . . Sp U , A = 0 2 1 0 : W . W = {( 2 5 a - b, - 1 5 a - b, a, b) | a, b R} , - , , ( 2 5 a - b, - 1 5 a - b, a, b) = a ( 2 5 , - 1 5 ,1, 0) + b(-1, -1, 0,1) , (-1, -1, 0,1) - ( 2 5 , - 1 5 ,1, 0) W . Sp({( 2 5 , - 1 5 ,1, 0), (-1, -1, 0,1)}) = W .W 4 5 . S = {(a, a - 2b, b) | a, b R}, T = {(3d , -d , 2d ) | d R} :( 0 ) S T , (3, -1, 2) = (3d , -d , 2d ) T (3, -1, 2) = (a, a - 2b, b) {0} , R 3 = S T .1 S , a = 3, b = 2, d = 1 (3, . 0 -1, 2) S T 2 3 , , p (-1) = p (0) = p (1) . p ( x) = a0 + a1 x + a2 x + a3 x W .2 3 . p ( x) = a0 + a1 x - a1 x : . a2 = 0, a3 = - a1 , . a0 - a1 + a2 - a3 = a0 a0 + a1 + a2 + a3 = a0 : R 4 [ x] - W - . W - , W z 3 3 . p ( x) = a0 + a1 x - a1 x , q ( x ) = b0 + b1 x - b1 x W ...
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This note was uploaded on 07/23/2009 for the course MATH. 04101 taught by Professor ישראלפרידמן during the Summer '06 term at The Open University.

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