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Консультация № 159962
08.02.2009, 21:47
0.00 руб.
0
1
1
Здравсвуйте.
Неделя до сессии, помогите пожалуйста с решением задачи:
Даны два линейных преобразования:
x1'=a11x1+a12x2+a13x3, x1''=b11'x1'+b12x2'+b13x3'
{ x2'=a21x1+a22x2+a23x3, x2''=b21x1'+b22x2'+b23x3'
x3'=a31x1+a32x2+a33x3, x3''=b31x1'+b32x2'+b33x3'
Средствами матричного исчисления найти преобразование, выражающее x1'', x2'', x3'' через x1, x2, x3.
x1'=4x1+3x2+2x3 x1''=x1'-2x2'-x3'
{ x2'=-2x1+x2-x3 { x2''=3x1'+x2'+2x3'
x3'=3x1+x2+x3 x3''=x1'+2x2'+2x3'
Неделя до сессии, помогите пожалуйста с решением задачи:
Даны два линейных преобразования:
x1'=a11x1+a12x2+a13x3, x1''=b11'x1'+b12x2'+b13x3'
{ x2'=a21x1+a22x2+a23x3, x2''=b21x1'+b22x2'+b23x3'
x3'=a31x1+a32x2+a33x3, x3''=b31x1'+b32x2'+b33x3'
Средствами матричного исчисления найти преобразование, выражающее x1'', x2'', x3'' через x1, x2, x3.
x1'=4x1+3x2+2x3 x1''=x1'-2x2'-x3'
{ x2'=-2x1+x2-x3 { x2''=3x1'+x2'+2x3'
x3'=3x1+x2+x3 x3''=x1'+2x2'+2x3'
Обсуждение
Неизвестный
09.02.2009, 09:23
общий
это ответ
Здравствуйте, Мария Романова!
X'=AX
X''=BX'=B(AX)=(BA)X
X=
(x1)
(x2)
(x3)
X'=
(x1')
(x2')
(x3')
X''=
(x1'')
(x2'')
(x3'')
A=
(4....3....2)
(-2...1...-1)
(3....1....1)
B=
(1...-2...-1)
(3....1....2)
(1....2....2)
X''=
(1...-2...-1)...(4....3....2).....(x1)...(5....0....3).....(x1)
(3....1....2).*.(-2...1...-1).*.(x2)=(16..12...7).*.(x2)
(1....2....2)....(3....1....1).....(x3)..(6.....7....2)....(x3)
Значит преобразование выглядит следующим образом
x1''=5x1+3x3
x2''=16x1+12x2+7x3
x3''=6x1+7x2+2x3
X'=AX
X''=BX'=B(AX)=(BA)X
X=
(x1)
(x2)
(x3)
X'=
(x1')
(x2')
(x3')
X''=
(x1'')
(x2'')
(x3'')
A=
(4....3....2)
(-2...1...-1)
(3....1....1)
B=
(1...-2...-1)
(3....1....2)
(1....2....2)
X''=
(1...-2...-1)...(4....3....2).....(x1)...(5....0....3).....(x1)
(3....1....2).*.(-2...1...-1).*.(x2)=(16..12...7).*.(x2)
(1....2....2)....(3....1....1).....(x3)..(6.....7....2)....(x3)
Значит преобразование выглядит следующим образом
x1''=5x1+3x3
x2''=16x1+12x2+7x3
x3''=6x1+7x2+2x3
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