2- A e B são duas matrizes quadradas de ordem 2, cujos os elementos são dados por bij= (i+J)2 e aij= 3i – 2j. Calcule A + B e 2A – 3B
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Olá,
Construindo as matrizes:
![A= \left[\begin{array}{cc}a_{11}&a_{12}\\a_{21}&a_{22}\end{array}\right] B= \left[\begin{array}{cc}b_{11}&b_{12}\\b_{21}&b_{22}\end{array}\right]](https://tex.z-dn.net/?f=A%3D+++%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Da_%7B11%7D%26amp%3Ba_%7B12%7D%5C%5Ca_%7B21%7D%26amp%3Ba_%7B22%7D%5Cend%7Barray%7D%5Cright%5D+B%3D++%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Db_%7B11%7D%26amp%3Bb_%7B12%7D%5C%5Cb_%7B21%7D%26amp%3Bb_%7B22%7D%5Cend%7Barray%7D%5Cright%5D+ "A= \left[\begin{array}{cc}a_{11}&a_{12}\\a_{21}&a_{22}\end{array}\right] B= \left[\begin{array}{cc}b_{11}&b_{12}\\b_{21}&b_{22}\end{array}\right]")
Obedecendo a condição (aij) = 3.i-2.j
Obedecendo a condição (bij) = (i+j).2
Sendo assim:
![A= \left[\begin{array}{cc}1&-1\\4&2\end{array}\right] B= \left[\begin{array}{cc}4&6\\6&8\end{array}\right]](https://tex.z-dn.net/?f=A%3D+++%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%26amp%3B-1%5C%5C4%26amp%3B2%5Cend%7Barray%7D%5Cright%5D+++B%3D+++%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D4%26amp%3B6%5C%5C6%26amp%3B8%5Cend%7Barray%7D%5Cright%5D+ "A= \left[\begin{array}{cc}1&-1\\4&2\end{array}\right] B= \left[\begin{array}{cc}4&6\\6&8\end{array}\right]")
Fazendo a soma das matrizes (A+B):
![\left[\begin{array}{cc}1&-1\\4&2\end{array}\right] +\left[\begin{array}{cc}4&6\\6&8\end{array}\right] = \left[\begin{array}{cc}5&5\\10&10\end{array}\right]](https://tex.z-dn.net/?f=++%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%26amp%3B-1%5C%5C4%26amp%3B2%5Cend%7Barray%7D%5Cright%5D++%2B%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D4%26amp%3B6%5C%5C6%26amp%3B8%5Cend%7Barray%7D%5Cright%5D+%3D+++%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D5%26amp%3B5%5C%5C10%26amp%3B10%5Cend%7Barray%7D%5Cright%5D+ "\left[\begin{array}{cc}1&-1\\4&2\end{array}\right] +\left[\begin{array}{cc}4&6\\6&8\end{array}\right] = \left[\begin{array}{cc}5&5\\10&10\end{array}\right]")
Multiplicação/Subtração de matrizes (2A - 3B):
![2. \left[\begin{array}{cc}1&-1\\4&2\end{array}\right] - 3. \left[\begin{array}{cc}4&6\\6&8\end{array}\right]](https://tex.z-dn.net/?f=2.++%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%26amp%3B-1%5C%5C4%26amp%3B2%5Cend%7Barray%7D%5Cright%5D+-+3.++%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D4%26amp%3B6%5C%5C6%26amp%3B8%5Cend%7Barray%7D%5Cright%5D+ "2. \left[\begin{array}{cc}1&-1\\4&2\end{array}\right] - 3. \left[\begin{array}{cc}4&6\\6&8\end{array}\right]")
\\
![\left[\begin{array}{cc}2&-2\\8&4\end{array}\right] - \left[\begin{array}{cc}3&6\\24&27\end{array}\right] = \left[\begin{array}{cc}-1&-8\\-16&-23\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D2%26amp%3B-2%5C%5C8%26amp%3B4%5Cend%7Barray%7D%5Cright%5D+-++%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D3%26amp%3B6%5C%5C24%26amp%3B27%5Cend%7Barray%7D%5Cright%5D+%3D+++%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-1%26amp%3B-8%5C%5C-16%26amp%3B-23%5Cend%7Barray%7D%5Cright%5D+ "\left[\begin{array}{cc}2&-2\\8&4\end{array}\right] - \left[\begin{array}{cc}3&6\\24&27\end{array}\right] = \left[\begin{array}{cc}-1&-8\\-16&-23\end{array}\right]")
Espero ter ajudado, bons estudos!
Construindo as matrizes:
Obedecendo a condição (aij) = 3.i-2.j
Obedecendo a condição (bij) = (i+j).2
Sendo assim:
Fazendo a soma das matrizes (A+B):
Multiplicação/Subtração de matrizes (2A - 3B):
Espero ter ajudado, bons estudos!
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