Question

Encontre a matriz X, na equação A . X = B, onde:
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Answer 1

$\large\boxed{\begin{array}{l}\rm Encontre~a~matrix~X, na~equac_{\!\!,}\tilde ao~A\cdot X=B,onde:\\\rm A=\begin{pmatrix}\sf2&\sf-3\\\sf3&\sf1\\\sf0&\sf5\end{pmatrix}~~~~~~B=\begin{pmatrix}\sf4&\sf3\\\sf6&\sf1\\\sf5&\sf0\end{pmatrix}\end{array}}$

$\large\boxed{\begin{array}{l}\underline{\rm soluc_{\!\!,}\tilde ao\!:}\\\sf O~produto~de~matrizes~existe~se,e~somente~se,\\\sf o~n\acute umero~de~colunas~da~1^a~matriz~for~igual\\\sf ao~n\acute umero~de~linhas~da~2^a~matriz.\\\sf A~matriz~resultante~ter\acute a~o~n\acute umero~de~linhas~da~1^a\\\sf e~o~n\acute umero~de~colunas~da~2^a\\\sf matematicamente:\\\sf A_{a\times b}\cdot B_{b\times c}=C_{a\times c}\end{array}}$

$\boxed{\begin{array}{l}\sf Perceba~que~a~matriz~X~deve~ser~do~tipo~2\times2\\\sf pois~A_{3\times2}\cdot X_{2\times2}=C_{3\times2}\\\sf assim~denotando~a~matriz~X~por~X=\begin{pmatrix}\sf a&\sf b\\\sf c&\sf d\end{pmatrix}~temos:\end{array}}$

$\boxed{\begin{array}{l}\begin{pmatrix}\sf2&\sf-3\\\sf3&\sf1\\\sf0&\sf5\end{pmatrix}\cdot\begin{pmatrix}\sf a&\sf b\\\sf c&\sf d\end{pmatrix}=\begin{pmatrix}\sf4&\sf3\\\sf6&\sf1\\\sf5&\sf0\end{pmatrix}\\\begin{pmatrix}\sf2a-3c&\sf2b-3d\\\sf3a+c&\sf3b+d\\\sf5c&\sf5d\end{pmatrix}=\begin{pmatrix}\sf4&\sf3\\\sf6&\sf1\\\sf5&\sf0\end{pmatrix}\end{array}}$

$\boxed{\begin{array}{l}\begin{cases}\sf2a-3c=4\\\sf3a+c=6\\\sf5c=5\end{cases}\\\sf perceba~que~este~sistema~\acute e~imposs\acute ivel~e~portanto\\\sf a~matrix~X~n\tilde ao~existe\end{array}}$