Question

OPERAÇÕES COM MATRIZES (adição e subtração) Exercícios: Efetue as operações

Answer 1

Resposta:

a) $\left[\begin{array}{cc}5&3\\4&2\\\end{array}\right] + \left[\begin{array}{cc}4&7\\6&9\\\end{array}\right] = \left[\begin{array}{cc}9&10\\10&11\\\end{array}\right]$

b) $\left[\begin{array}{cc}5&3\\4&2\\\end{array}\right] - \left[\begin{array}{cc}4&7\\6&9\\\end{array}\right] = \left[\begin{array}{cc}1& -4\\-2&-7\\\end{array}\right]$

c) $\left[\begin{array}{ccc}10&20&-11\\11&21&-13\\12&22&-17\end{array}\right] +\left[\begin{array}{ccc}5&19&5\\6&23&20\\7&27&17\end{array}\right] = \left[\begin{array}{ccc}15&39&-6\\17&44&7\\19&49&0\end{array}\right]$

d)$\left[\begin{array}{ccc}10&20&-11\\11&21&-13\\12&22&-17\end{array}\right] -\left[\begin{array}{ccc}5&19&5\\6&23&20\\7&27&17\end{array}\right] = \left[\begin{array}{ccc}5&1&-16\\5&-2&-33\\5&-5&-34\end{array}\right]$

e) $\left[\begin{array}{cc}-9&3\\-4&2\\\end{array}\right] - \left[\begin{array}{cc}-8&11\\10&-19\\\end{array}\right] = \left[\begin{array}{cc}-1& -8\\-14&21\\\end{array}\right]$

Explicação passo-a-passo:

Se soma cada um dos termos correspondentes entre as matrizes que possuem a mesma quantidade tanto de linhas, quanto de colunas. Exemplo com o item a):

$\left[\begin{array}{cc}5&3\\4&2\\\end{array}\right] + \left[\begin{array}{cc}4&7\\6&9\\\end{array}\right] = \left[\begin{array}{cc}9&10\\10&11\\\end{array}\right]\\\\a11 + b11 = 5 + 4 = 9 \\a12 + b12 = 3 + 7 = 10 \\a21 + b21 = 4 + 6 = 10\\a22 + b22 = 2 + 9 = 11$