4
Semana 4

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A operação de soma de matrizes e de multiplicação por escalar são definidas da mesma forma que definimos estas operações para vetores. Na soma, basta somar componente a componente, enquanto que na multiplicação por escalar o que fazemos é multiplicar todas as componentes da matriz pelo escalar (número) dado. Desta forma, por exemplo, $$\begin{array}{llll}\hfill \left[\begin{array}{cccc}\hfill 1\hfill & \hfill -1\hfill & \hfill \pi \hfill & \hfill 0\hfill \\ \hfill 11\hfill & \hfill 11\hfill & \hfill -2\hfill & \hfill 0\hfill \\ \hfill 9\hfill & \hfill 0\hfill & \hfill 4\hfill & \hfill 4\hfill \\ \hfill \hfill \end{array}\right]+\left[\begin{array}{cccc}\hfill 1\hfill & \hfill 4\hfill & \hfill 1\hfill & \hfill 9\hfill \\ \hfill -5\hfill & \hfill 10\hfill & \hfill 2\hfill & \hfill 11\hfill \\ \hfill -3\hfill & \hfill 8\hfill & \hfill 0\hfill & \hfill -6\hfill \\ \hfill \hfill \end{array}\right]& =\left[\begin{array}{cccc}\hfill 1+1\hfill & \hfill -1+4\hfill & \hfill \pi +1\hfill & \hfill 0+9\hfill \\ \hfill 11-5\hfill & \hfill 11+10\hfill & \hfill -2+2\hfill & \hfill 0+11\hfill \\ \hfill 9-3\hfill & \hfill 0+8\hfill & \hfill 4+0\hfill & \hfill 4-6\hfill \\ \hfill \hfill \end{array}\right]& \hfill & \\ \hfill & =\left[\begin{array}{cccc}\hfill 2\hfill & \hfill 3\hfill & \hfill \pi +1\hfill & \hfill 9\hfill \\ \hfill 6\hfill & \hfill 21\hfill & \hfill 0\hfill & \hfill 11\hfill \\ \hfill 6\hfill & \hfill 8\hfill & \hfill 4\hfill & \hfill -2\hfill \\ \hfill \hfill \end{array}\right]& \hfill & \end{array}$$

enquanto

$$5\cdot \left[\begin{array}{cccc}\hfill 1\hfill & \hfill 4\hfill & \hfill 1\hfill & \hfill 9\hfill \\ \hfill -5\hfill & \hfill 10\hfill & \hfill 2\hfill & \hfill 11\hfill \\ \hfill -3\hfill & \hfill 8\hfill & \hfill 0\hfill & \hfill -6\hfill \\ \hfill \hfill \end{array}\right]=\left[\begin{array}{cccc}\hfill 5\cdot 1\hfill & \hfill 5\cdot 4\hfill & \hfill 5\cdot 1\hfill & \hfill 5\cdot 9\hfill \\ \hfill 5\cdot \left(-5\right)\hfill & \hfill 5\cdot 10\hfill & \hfill 5\cdot 2\hfill & \hfill 5\cdot 11\hfill \\ \hfill 5\cdot \left(-3\right)\hfill & \hfill 5\cdot 8\hfill & \hfill 5\cdot 0\hfill & \hfill 5\cdot \left(-6\right)\hfill \\ \hfill \hfill \end{array}\right]=\left[\begin{array}{cccc}\hfill 5\hfill & \hfill 20\hfill & \hfill 5\hfill & \hfill 45\hfill \\ \hfill -25\hfill & \hfill 50\hfill & \hfill 10\hfill & \hfill 55\hfill \\ \hfill -15\hfill & \hfill 40\hfill & \hfill 0\hfill & \hfill -30\hfill \\ \hfill \hfill \end{array}\right].$$

(4.1)

Exercícios resolvidos

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Exercícios

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