Question

dadas las siguientes matrices

A=$\left[\begin{array}{ccc}-2&1&4\\1&-3&5\\5&-2&-7\end{array}\right] B=\left[\begin{array}{ccc}0&-1&4\\1&-2&6\\-4&-1&5\end{array}\right] C= \left[\begin{array}{ccc}-3&1&-2\\2&0&-6\\4&-1&5\end{array}\right]$

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$A) (A^{T} + C ) . (2A+B)\\\\B) (A+C^{T} )^{T} . 3B$

Answer 1

$A)(A^T+C).(2A+B)=$

$(\left[\begin{array}{ccc}-2&1&4\\1&-3&5\\5&-2&-7\end{array}\right]^T+\left[\begin{array}{ccc}-3&1&-2\\2&0&-6\\4&-1&5\end{array}\right]).(2.\left[\begin{array}{ccc}-2&1&4\\1&-3&5\\5&-2&-7\end{array}\right]+\left[\begin{array}{ccc}0&-1&4\\1&-2&6\\-4&-1&5\end{array}\right])=$$(\left[\begin{array}{ccc}-2&1&5\\1&-3&-2\\4&5&-7\end{array}\right]+\left[\begin{array}{ccc}-3&1&-2\\2&0&-6\\4&-1&5\end{array}\right]).(\left[\begin{array}{ccc}-4&2&8\\2&-6&10\\10&-4&-14\end{array}\right] +\left[\begin{array}{ccc}0&-1&4\\1&-2&6\\-4&-1&5\end{array}\right])=$

$\left[\begin{array}{ccc}-5&2&3\\3&-3&-8\\8&4&-2\end{array}\right] .\left[\begin{array}{ccc}-4&1&12\\3&-8&16\\6&-5&-9\end{array}\right]=$

$\left[\begin{array}{ccc}-5.(-4)+2.4+3.6&-5.1+2.(-8)+3.(-5)&-5.(12)+2.16+3.(-9)\\3.(-4)-3.3-8.6&3.1-3.(-8)-8.(-5)&3.12-3.16-8.(-9)\\8.(-4)+4.3-2.6&8.1+4.(-8)-2.(-5)&8.12+4.16-2.(-9)\end{array}\right]=$

$\left[\begin{array}{ccc}46&-36&-55\\-69&67&60\\-32&-14&205\end{array}\right]$

$B)(A+C^T)^T.3B=$

$(\left[\begin{array}{ccc}-2&1&4\\1&-3&5\\5&-2&-7\end{array}\right]+\left[\begin{array}{ccc}-3&2&4\\1&0&-1\\-2&-6&5\end{array}\right])^T\times \left[\begin{array}{ccc}-9&3&-6\\6&0&-18\\12&-3&15\end{array}\right]=$

$\left[\begin{array}{ccc}-5&3&8\\2&-3&4\\3&-8&-2\end{array}\right] ^T\times \left[\begin{array}{ccc}-9&3&-6\\6&0&-18\\12&-3&15\end{array}\right]=$

$\left[\begin{array}{ccc}-5&2&3\\3&-3&-8\\8&4&-2\end{array}\right]\times \left[\begin{array}{ccc}-9&3&-6\\6&0&-18\\12&-3&15\end{array}\right]=$

$\left[\begin{array}{ccc}93&-24&39\\-141&33&-84\\-72&30&-150\end{array}\right]$

Espero que te sirva, saludos!