Question

se A= (-1   5 )              4   8                e  B= ( 0   -2)         6   -4  , qual é a matriz C de ordem 2, tal que: C+A/3 = B-C/5

Answer 1

$A= \left[\begin{array}{cc}-1&5\\4&8\end{array}\right] \\ B= \left[\begin{array}{cc}0&-2\\6&-4\end{array}\right]$

Seja C matriz quadrada de ordem 2 tal que $C+ \frac{1}{3} A=B- \frac{1}{5}C \\ C+ \frac{1}{5}C=B- \frac{1}{3}A \\ \frac{6}{5} C=B- \frac{1}{3}A \\ C= \frac{5}{6}B- \frac{5}{18}A \\ C= \frac{5}{6} \left[\begin{array}{cc}0&-2\\6&-4\end{array}\right] - \frac{5}{18} \left[\begin{array}{cc}-1&5\\4&8\end{array}\right] \\ C= \left[\begin{array}{cc}0&-5/3\\5&-10/3\end{array}\right] + \left[\begin{array}{cc}5/18&-25/18\\-10/9&-20/9\end{array}\right] = \left[\begin{array}{cc}5/18&-55/18\\35/9&-50/9\end{array}\right]$