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Консультация № 192261
27.12.2017, 21:31
0.00 руб.
0
3
1
Здравствуйте! Прошу помощи в следующем вопросе:
не могу понять как это все преобразуеться
Пусть λ – произвольное действительное число, а a ⃗(α;-α),b ⃗(β;-β) и – произвольные векторы пространства. Тогда λ*(a ⃗+b ⃗ )= λ((α;-α)+(β;-β))=λ*(α+β;-α-β)=(λ*(α+β);λ*(-α-β))=(λ*α+λ*β;λ*(-α)+λ*(-β))=(λ*α;λ*(-α))+(λ*β;λ*(-β))=λ*(α;-α)+λ*(β;-β)=λ*a ⃗+λ*b ⃗.
не могу понять как это все преобразуеться
Пусть λ – произвольное действительное число, а a ⃗(α;-α),b ⃗(β;-β) и – произвольные векторы пространства. Тогда λ*(a ⃗+b ⃗ )= λ((α;-α)+(β;-β))=λ*(α+β;-α-β)=(λ*(α+β);λ*(-α-β))=(λ*α+λ*β;λ*(-α)+λ*(-β))=(λ*α;λ*(-α))+(λ*β;λ*(-β))=λ*(α;-α)+λ*(β;-β)=λ*a ⃗+λ*b ⃗.
Обсуждение
28.12.2017, 07:00
общий
Адресаты:
Что Вам непонятно в записанном? Там доказывается, что произведение скаляра на сумму двух векторов равно сумме произведений этого скаляра на каждый из слагаемых векторов. При этом используются свойства умножения скаляра на координаты вектора.
Об авторе:
Facta loquuntur.
Facta loquuntur.
28.12.2017, 09:30
общий
это ответ
Здравствуйте, den666san!
В школьном учебнике геометрии А. В. Погорелова произведением вектора
на число 
называется вектор 
Суммой векторов и 
называется вектор 
Для действительных чисел имеет место распределительный закон умножения относительно сложения, то есть 
В силу того, что действия над векторами сводятся к действиям над координатами этих векторов, которые являются действительными числами, имеем
Тем самым доказан распределительный закон умножения числа на вектор относительно сложения векторов.
Если вместо векторов и взять векторы 
и 
то получится та цепочка равенств, которая вызвала у Вас вопросы. Она действительно выглядит странно, по-моему.
В школьном учебнике геометрии А. В. Погорелова произведением вектора
на число называется вектор Суммой векторов и называется вектор Для действительных чисел имеет место распределительный закон умножения относительно сложения, то есть В силу того, что действия над векторами сводятся к действиям над координатами этих векторов, которые являются действительными числами, имеемТем самым доказан распределительный закон умножения числа на вектор относительно сложения векторов.
Если вместо векторов
и взять векторы и то получится та цепочка равенств, которая вызвала у Вас вопросы. Она действительно выглядит странно, по-моему.
5
Об авторе:
Facta loquuntur.
Facta loquuntur.
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