Considere a matrizes
e
.
(b) Escolha matrizes-coluna
e
de modo que
seja um sistema linear compatível e
seja um sistema linear incompatível.
(b) Escolha matrizes-coluna
Passo 1
Beleza, vamos lá! A questão pede para a gente escolher duas matrizes-coluna,
e
, de forma que o sistema
seja compatível (ou seja, tenha solução) e o sistema
seja incompatível (não tenha solução). Vamos usar álgebra linear para isso, especificamente conceitos de sistemas lineares e espaços coluna das matrizes.
Passo 2
Primeiro, vamos entender o que significa um sistema ser compatível ou incompatível. Um sistema
é compatível se o vetor
estiver no espaço coluna da matriz
. Isso quer dizer que
pode ser escrito como uma combinação linear das colunas de
. Se não for possível, o sistema é incompatível.
Passo 3
Vamos analisar a matriz
dada:
Para saber o que está no espaço coluna de
, podemos verificar a combinação linear das colunas. Vamos chamar as colunas de
de
,
, e
.
Passo 4
Para escolher
que torna o sistema compatível, basta escolher
como uma combinação das colunas de
. Por exemplo, podemos escolher
, ou qualquer outra combinação.
Vamos fazer:
Passo 5
Agora, para escolher
de forma que o sistema seja incompatível, precisamos que
não esteja no espaço coluna de
. Uma maneira simples é escolher um vetor que não possa ser formado pelas combinações das colunas de
. Por exemplo, podemos escolher um vetor com uma componente extra ou que não satisfaça as equações formadas pelas colunas de
.
Vamos escolher:
Resposta
Escolhemos:
Exercícios relacionados
Uma placa quadrada de cobre com lados de
sem carga líquida é colocada em uma região de campo elétrico uniforme de
orientado perpendicularmente à placa. Encontre a carga total em cada face da placa. Use epsilon zero como
. De a resposta em C.
nenhuma das outras
For your examination, preferably print documents compiled from auto-multiple-choice.
nenhuma das outras
For your examination, preferably print documents compiled from auto-multiple-choice.
Considere um sistema linear
qualquer. Suponhamos que o processo de escalonamento de sua matriz completa é dado por
Com base nas informações acima, classifique as afirmações abaixo em verdadeiras ou falsas, aoresentando breve justificativa.
(d) Se a matriz possui uma linha de zeros, então o sistema linear
é incompatível.
(d) Se a matriz
Unidades eletrônicas de flash em uma câmera contém um capacitor para armazenar a energia usada para produzir o flash. Em tais unidades, o flash dura
s com uma potência média gerada de
. Se a conversão de energia elétrica em luz tem eficiência de
(o resto vai para energia térmica), quanta energia deve ser armazenada no capacitor para um flash?
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Uma casca cilíndrica isolante muito longa e de raio
está carregada com densidade linear dada por
distribuída uniformemente sobre sua superfície. Qual seria a leitura de um voltímetro ao liga-lo entre a superfície do cilindro e um ponto a uma distância de
acima de sua superfície?
nenhuma das outras
nenhuma das outras