MATRIZES: OPERA\303\207\303\225ES BASICAS
Revendo a Terminologia da matrizUma matriz \303\251 uma tabela retangular de n\303\272meros delimitada por colchetes ou parentes e \303\251 indicada por uma letra mai\303\272scula. Cada n\303\272mero da tabela \303\251 um elemento. As matrizes s\303\243o classificadas pela sua dimens\303\243o, que \303\251, o n\303\272mero de linhas e colunas que elas possuem. Por exemplo, uma matriz 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possui tr\303\252s linhas e quatro colunas, com dimens\303\243o 3 x 4. O n\303\272mero de linhas \303\251 sempre dado primeiro. Quando o n\303\272mero de linhas e colunas s\303\243o os mesmos, a matriz \303\251 uma matriz quadrada. Duas matrizes s\303\243o iguais se tiverem a mesma dimens\303\243o e se cada par de elementos correspondentes forem iguais.Estudando Adi\303\247\303\243o de Matrizes
As matrizes podem ser adicionadas ou subtra\303\255das somente se tiverem a mesma dimens\303\243o.
Dos 18 membros do time de luta escolar, 6 estavam acima do peso da classe. O treinador os informou que deveriam perder o excesso de peso nos pr\303\263ximos 10 dias ou seriam incapazes de participar do campeonato. Os pesos dos 6 lutadores acima do peso (H) e a quantidade correspondente que cada um deve perder (L) \303\251 dado nas matrizes H e L abaixo:
H = (194,154,177,214,188,138) ,
L = (9,4,12,14,8,8)O peso necess\303\241rio para cada um dos seis lutadores pode ser determinado pela subtra\303\247\303\243o da matriz L com a matriz O.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 os resultados
No final dos 10 dias, os seis lutadores deveriam pesar 185, 150, 165, 200, 180, e 130, respectivamente.
Depois que os seis lutadores acima deixaram de praticar, o treinador realizou uma mistura na ordem da quantidade de peso que cada jogador precisou perder. A altera\303\247\303\243o dessas quantidades \303\251 dada na matriz R.
R = (8,8,14,12,9,4)
Determine a altera\303\247\303\243o dos pesos de cada um dos seis lutadores.
R: H - R
186, 146, 163, 202, 179, 134
Quanto deveriam pesar cada um dos seis lutadores se fossem engordar o peso indicado na matriz R?
R: H + R
202, 162, 191, 226, 197, 142
Estudando Multiplica\303\247\303\243o Escalar
Multiplicar cada elemento de uma matriz por um n\303\272mero simples, denomina-se multiplica\303\247\303\243o escalar. As aplica\303\247\303\265es de multiplica\303\247\303\243o escalar s\303\243o facilmente encontradas em situa\303\247\303\265es di\303\241rias.
O primeiro round do tabuleiro de Jeopardy \303\251 semelhante ao seguinte.Musical
Cars Sports Movies Trivia Performers CDs
$100 $100 $100 $100 $100 $100
$200 $200 $200 $200 $200 $200
$300 $300 $300 $300 $300 $300
$400 $400 $400 $400 $400 $400
$500 $500 $500 $500 $500 $500
Uma matriz J representando o tabuleiro de Jeopardy \303\251 mostrada abaixo :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Para o segundo round de Jeopardy, todas as quantidades de d\303\263lares s\303\243o duplicadas. Isto pode ser mostrado utilizando a multiplica\303\247ao escalar.
R: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbW5HRiQ2JFEiMkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RJyZzZG90O0YnRi8vJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjgvJSlzdHJldGNoeUdGOC8lKnN5bW1ldHJpY0dGOC8lKGxhcmdlb3BHRjgvJS5tb3ZhYmxlbGltaXRzR0Y4LyUnYWNjZW50R0Y4LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGRy1JI21pR0YkNiVRIkpGJy8lJ2l0YWxpY0dRJXRydWVGJy9GMFEnaXRhbGljRicvJStleGVjdXRhYmxlR0Y4Ri8=
Encontre a matriz representando a quantidade de d\303\263lares para o terceiro round de Jeopardy.
R : LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbW5HRiQ2JFEiM0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RJyZzZG90O0YnRi8vJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjgvJSlzdHJldGNoeUdGOC8lKnN5bW1ldHJpY0dGOC8lKGxhcmdlb3BHRjgvJS5tb3ZhYmxlbGltaXRzR0Y4LyUnYWNjZW50R0Y4LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGRy1JI21pR0YkNiVRIkpGJy8lJ2l0YWxpY0dRJXRydWVGJy9GMFEnaXRhbGljRicvJStleGVjdXRhYmxlR0Y4Ri8=
Descreva a matriz tripla de Jeopardy.
Os valores s\303\243o o triplo do tabuleiro original de Jeopardy.Um artigo de jornal recente mostrou estat\303\255sticas criminais nos Estados Unidos entrevistando cerca de 100.000 pessoas em intervalos de cinco anos entre 1975 e 1995.
1975 1980 1985 1990 1995
Burglary 1322 1430 1203 1201 1197
Car theft 450 500 421 662 712
Robbery 193 201 203 247 273
Este dado pode ser expressado na matriz S.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 jornal posteriormente organizou uma breve corre\303\247\303\243o indicando que aquelas estat\303\255sticas estavam defasadas em 15%.
Usar a multiplica\303\247\303\243o escalar para encontrar a matriz correta e dar o resultado.R: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbW5HRiQ2JFElMS4xNUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RJyZzZG90O0YnRi8vJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjgvJSlzdHJldGNoeUdGOC8lKnN5bW1ldHJpY0dGOC8lKGxhcmdlb3BHRjgvJS5tb3ZhYmxlbGltaXRzR0Y4LyUnYWNjZW50R0Y4LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGRy1JI21pR0YkNiVRIlNGJy8lJ2l0YWxpY0dRJXRydWVGJy9GMFEnaXRhbGljRicvJStleGVjdXRhYmxlR0Y4Ri8=Veja a matriz 1.15 S.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 Multiplica\303\247\303\243o de Matriz
O produto de duas matrizes \303\251 chamado de produto linha-por-coluna. Cada elemento na matriz produto \303\251 obtido pelo somat\303\263rio do produto dos elementos da linha de A pelos elementos da coluna de B. A matriz produto pode ser encontrada somente se o n\303\272mero de colunas de A for igual ao n\303\272mero de linhas de B. O produto final ter\303\241 tantas linhas quanto A e tantas colunas quanto B. Por exemplo, o produto de uma matriz 3 x 5 com uma 5 x 4 \303\251 uma matriz 3 x 4.
Considere a situa\303\247\303\243o onde a padaria de Bella vende quatro itens principais: massas, p\303\243es, bolos e tortas. A quantidade de cada ingrediente (em x\303\255caras, exceto os ovos) usado para preparar estes \303\255tens \303\251 dado abaixo:
Eggs Flour Sugar Shortening MilkConsidere a situa\303\247\303\243o onde a padaria de Bella vende quatro itens principais: massas, p\303\243es, bolos e tortas. A quantidade de cada ingrediente (em x\303\255caras, exceto os ovos) usado para preparar estes \303\255tens \303\251 dado abaixo:
Eggs Flour Sugar Shortening Milk
Pastries (dozen) 1 3 1/2 1/4 3/4
Bread (loaf) 0 3 0 1/4 0
Cakes (three - layer) 4 3 2 3/4 1
Pies (crust & filling) 3 1 2 1/3 1.5
O pre\303\247o (em centavos) para cada ingrediente quando comprado em grandes e pequenas quantidades \303\251 listado abaixo:
Large Cost Small Cost
Eggs 5 4
Flour 8 10
Sugar 12 14
Shortening 14 18
Milk 6 9
A Multiplica\303\247\303\243o de Matrizes pode ser usada para encontrar um pre\303\247o comparativo por item para as duas op\303\247\303\265es de compra.
Indicar a quantidade de cada ingrediente pela matriz M e o pre\303\247o pela matriz C.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O produto das matrizes M C abaixo representa o pre\303\247o total por item para as duas opera\303\247\303\265es de compra.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 matriz resultante representa o pre\303\247o de grandes e pequenas quantidades para a prepara\303\247\303\243o de uma d\303\272zia de massas, uma bisnaga de p\303\243o, um bolo de tr\303\252s camadas e uma torta. Por exemplo, o pre\303\247o de uma grande quantidade de massas \303\251 43 centavos.
Qual o pre\303\247o de uma grande quantidade de bisnagas de p\303\243o?
R: 27.5 centavos.
Qual o pre\303\247o de uma pequena quantidade de um bolo de tr\303\252s camadas?
R: 96.5 centavos.
Suponha que as encomendas das quartas-feiras consista em 30 d\303\272zias de massas, 150 bisnagas, 45 bolos e 50 tortas. Esta ordem pode ser escrita como uma matriz W.
W = (30,150,45,50)
A quantidade necess\303\241ria de cada ingrediente para preencher as encomendas do dia pode ser calculado usando a multiplica\303\247\303\243o das matrizes .Aprofundando Seus Conhecimentos
A dimens\303\243o da soma de duas matrizes \303\251 igual a dimens\303\243o de cada matriz original.
Descreva todas as dimens\303\265es poss\303\255veis para uma matriz com 8 entradas.
R: 1 x 8, 2 x 4, 4 x 2, e 8 x 1
Amatriz resultante tem elementos num\303\251ricos inteiros. Descreva os elementos da matriz B.
R: Os elementos da matriz B s\303\243o multiplicados por 4.
Explique como a multiplica\303\247\303\243o escalar \303\251 diferente da multiplica\303\247\303\243o de dois n\303\272meros.