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O desenvolvimento da teoria das matrizes deu-se no século XIX, na Inglaterra, associado aos nomes de Arthur Cayley e James Sylvester.
Hoje, em quase todos os jornais e revistas é possível encontrar tabelas informativas. Na Matemática chamamos estas tabelas de MATRIZES.
As Matrizes são, portanto, apresentadas por linhas e colunas em uma tabela.
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CONCEITO DE MATRIZ.É todo o quadro de elementos dispostos em linhas e em colunas, ou seja, matrizes são tabelas de números reais, utilizadas nas mais diversas áreas do conhecimento: Matemática, Física, Estatística, Computação, Economia, Ciências Contábeis, Administração, Agronomia, Zootecnia, eletrônica, na análise de insumo-produto e nos diversos ramos de engenharia, dentre outros setores.
A (aij) mxnNome Matriz
Elementos de Linha e Coluna
(mxn)= Nº de linhas e Nº de colunas
Ordem matriz.
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Nome da matriz: Letra maiúscula do alfabeto.
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Introdução ao estudo de matrizes
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Introdução ao estudo de matrizes
M
T
N
1º 2º 3º 4º 5º
37,3 C
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i= Linha j= Coluna
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Etc . . .
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Notas de João e Maria
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Os dados referentes a altura, peso e idade de um grupo de quatro pessoas podem ser expressos pela tabela.
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Representação matemática de uma matriz.
Uso de parênteses, colchetes ou barras duplas.
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Veja o resultado do aproveitamento escolar de 4 turmas diferentes na tabela, com as respectivas disciplinas e o aproveitamento de cada turma por disciplina.
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Considere a Tabela abaixo, na qual estão colocados os estoques dos produtos A, B, C e D nas lojas 1, 2, 3.
Informações contidas na tabela.
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Nesse caso, a matriz possui 3 linhas e 4 colunas, e representa-se assim: 12 Elementos.
A=
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Um conglomerado é composto por 5 lojas numeradas e 1 a 5. A tabela a seguir apresenta o faturamento, em reais, nos 4 primeiros dias do mês de agosto de um determinado ano.
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Problema anterior . . . 2.800,00
11.900,007.700,00Soma a coluna Soma a linha
Segue . .
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2.000
2.000
2.900
1.900
2.450
2.500 3.000
20 elementos na matriz
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DP=1
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matrizA construção de uma matriz é feita conhecendo-se
uma relação entre os índices da matriz genérica.
-1
3
6
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matriz
4) Escreva as matrizes.
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matriz
Respostas das atividades.
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matriz
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Funciona como elemento neutro na adição de
matrizes.
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IGUALDADE DE MATRIZES.Calcular ‘a’; ‘b’ e ‘c’ para que A=B.
A= - 4/3; b= - 10/3 e c=5
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ADIÇÃO DE MATRIZES.
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Subtração:
Adição:
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Multiplica-se o escalar por cada elemento da matriz.
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Resposta.Proposto.
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Proposto. Resposta.
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Apostila.
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Respostas …. Abaixo.
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Multiplique as matrizes, caso exista o produto.
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Multiplique as matrizes, caso exista o produto.
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Multiplique as matrizes, caso exista o produto.
Para fixação da aprendizagem.
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Ok. São inversas.
Condição:Determinante
ǂ 0
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Condição:Determinante
ǂ 0
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MATRIZ INVERSA.
Lembrando que: (DP) . (DS) tem que ser difrente de ZERO.
Ou seja: Determinante diferente de ZERO.Calcular, caso exista, a inversa da matriz.
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MATRIZ INVERSA.Calcular, caso exista, a inversa da matriz.
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MATRIZ INVERSA.
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DESAFIO:
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DESAFIO:
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APLICAÇÕES DO ESTUDO DAS MATRIZES….APLICAÇÕES DO ESTUDO de Sistemas Lineares
OUTRO ARQUIVO, Ok.