MATRIZES OPERAÇÕES COM MATRIZES EP 1

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Operações com matrizes: adição e subtração e multiplicação de uma matriz por um número real. • Operações com Matrizes • Adição de matrizes • A adição de matrizes é definida apenas para matrizes de mesma ordem, Assim, se A = (aij)m×n e B = (bij)m×n , diz-se que a soma de A + B é dada pela matriz C = (cij)m×n, sendo cij = aij + bij para todo i compreendido no intervalo 1 ≤ i ≤ m e para todo j compreendido no intervalo 1 ≤ j ≤ n. • Propriedades da adição • Considerando as matrizes A, B, C e O (matriz nula), ambas de mesma ordem, valem: • A + B = B + A (comutativa) • (A + B) + C = A + (B + C) (associativa) • A + 0 = 0 + A = A (existência do elemento neutro) • A + (-A) = (-A) + A = 0 (existência do elemento oposto) • A + C = B + C ⇔ A = B (cancelamento) • Subtração de matrizes • A subtração entre duas matrizes A e B, ambas de mesma ordem, é obtida a partir da soma da matriz A com a oposta de B, ou seja, A – B = A + (-B). • Multiplicação de um número real por uma matriz • Seja a matriz A e k um número real, diz-se que k • A é uma matriz do tipo m X n, obtida a partir do produto entre k e todos os elementos da matriz A. • Observação: • Dadas duas matrizes A e B, o produto AB só poderá ser obtido se o número de colunas de A for igual ao número de linhas de B. A matriz resultante terá como ordem o número de linhas de A e o número de colunas de B. • Matriz inversa • Uma matriz quadrada A de ordem n é a inversa da matriz quadrada A, também de ordem n, se satisfizer a seguinte condição: • -------------------------------------------------------- • tags: operações com matrizes exercícios, operações com matrizes adição subtração e multiplicação, operações com matrizes pdf, operações com matrizes multiplicação, • matrizes determinantes, operações com matrizes doc, tipos de matrizes, matriz inversa, operações com matrizes, multiplicação de matrizes, matriz, matrizes,adição e subtração de matrizes, soma de matrizes, igualdade de matrizes, adição de matrizes, subtração de matrizes, operação com matrizes, divisão de matrizes,soma e subtração de matrizes, soma de matriz, operações com matrizes, matrizes adição e subtração, matriz inversa me salva, operações com matrizes, igualdade de matriz, operações com matrizes exercícios, operações com matrizes 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