Question

1)     Dadas as matrizes A = , B = e C = , calcule o resultado das seguintes operações:

a) 2A – B +3C                                                          b)1/2A-(1/3B+C)

 

A= (0 4 -2)             B=(-3 6 9)             C=(0 -1 0)

      (6 2 8)                   (12 -6 0)                (1 -1 2)

Answer 1

Olá, tudo bem?

 

Dados os valores das matrizes, os cálculos e resultados são os seguintes:

a) 2A – B + 3C

$2 . \left[\begin{array}{ccc}0&4&-2\\6&2&8\end{array}\right] - \left[\begin{array}{ccc}-3&6&9\\12&-6&8\end{array}\right]+3.\left[\begin{array}{ccc}0&-1&0\\1&-1&2\end{array}\right] \\=\left[\begin{array}{ccc}0&8&-4\\12&4&16\end{array}\right]- \left[\begin{array}{ccc}-3&6&9\\12&-6&8\end{array}\right]+\left[\begin{array}{ccc}0&-3&0\\3&-3&6\end{array}\right] \\ =\left[\begin{array}{ccc}3&-2&-13\\0&10&16\end{array}\right]+ \left[\begin{array}{ccc}0&-3&0\\3&-3&6\end{array}\right] \\ =\left[\begin{array}{ccc}3&-1&-13\\3&7&22\end{array}\right]$

b)/2A-(1/3B+C)

$\frac{1}{2}. \left[\begin{array}{ccc}0&4&-2\\6&2&8\end{array}\right] - ( \frac{1}{3}.\left[\begin{array}{ccc}-3&6&9\\12&-6&8\end{array}\right]+\left[\begin{array}{ccc}0&-1&0\\1&-1&2\end{array}\right]) \\ = \left[\begin{array}{ccc}0&4&-1\\3&1&4\end{array}\right] - ( \frac{1}{3}.\left[\begin{array}{ccc}-3&5&9\\13&-7&10\end{array}\right] )\\ = \left[\begin{array}{ccc}0&4&-1\\3&1&4\end{array}\right] - \left[\begin{array}{ccc}-1& \frac{5}{3}&3\\ \frac{13}{3}& \frac{-7}{3}& \frac{10}{3}\end{array}\right]\\=\left[\begin{array}{ccc}1& \frac{7}{3}&-4\\ \frac{-4}{3}& \frac{10}{3}& \frac{2}{3}\end{array}\right]$

Espero ter ajudado!