Question

MATRIZES

Atividade para ser entregue:

Answer 1

$\Large\boxed{\begin{array}{l}\rm 1)~\sf Matrizes~\acute e~o~conjunto~de~n\acute umeros\\\sf dispostos~em~tabelas~compostas~por\\\sf linhas~e~colunas.\\\underline{\rm exemplo}~\begin{bmatrix}\sf1&\sf0\\\sf0&\sf1\end{bmatrix}\end{array}}$

$\Large\boxed{\begin{array}{l}\rm 2)~\sf em~uma~matriz~da~forma~A(a_{ij})_{m\times n}\\\sf as~letras~~m~e~n~s\tilde ao~respectivamente\\\sf a~linha~e~a~coluna~da~matriz.\end{array}}$

$\Large\boxed{\begin{array}{l}\rm 3)~\sf Matriz~identidade~\acute e~a~~matriz~~cuja~diagonal~principal\\\sf \acute e~formada~somente~pelo~n\acute umero~1.\\\underline{\rm exemplo:}\\\\\sf I_3=\begin{bmatrix}\sf1&\sf0&\sf0\\\sf0&\sf1&\sf0\\\sf 0&\sf0&\sf1\end{bmatrix}\end{array}}$

$\Large\boxed{\begin{array}{l}\rm 4)~\sf Matriz~transposta~\acute e~a~matriz~obtida\\\sf trocando-se~as~linhas~por~colunas.\\\sf indica-se~por~A^T\\\sf sendo~A~uma~matriz~qualquer.\\\underline{\rm exemplo:}\\\\\sf A=\begin{bmatrix}\sf 1&\sf2&\sf3\\\sf 4&\sf5&\sf6\end{bmatrix}\\\sf A^T=\begin{bmatrix}\sf1&\sf4\\\sf2&\sf5\\\sf3&\sf6\end{bmatrix}\end{array}}$

$\Large\boxed{\begin{array}{l}\rm 5)~\sf Para~que~duas~matrizes~sejam~iguais\\\sf \acute e~necess\acute ario~que~sejam~do~mesmo~tipo\\\sf e~os~elementos~de~mesma~posic_{\!\!,}\tilde ao\\\sf sejam~iguais.\end{array}}$

$\Large\boxed{\begin{array}{l}\underline{\rm exemplo:}\\\sf A=\begin{bmatrix}\sf a_{11}&\sf a_{12}\\\sf a_{21}&\sf a_{22}\end{bmatrix}~B=\begin{bmatrix}\sf b_{11}&\sf b_{12}\\\sf b_{21}&\sf b_{22}\end{bmatrix}\\\sf A=B\Longleftrightarrow\begin{cases}\sf a_{11}=b_{11}\\\sf a_{12}=b_{12}\\\sf a_{21}=b_{21}\\\sf a_{22}=b_{22}\end{cases}\end{array}}$

$\Large\boxed{\begin{array}{l}\rm 6)~\sf Os~monitores~de~supermercado~e~as~planilhas\\\sf de~excel~nos~d\tilde ao~ ideias~de~matrizes\end{array}}$

$\Large\boxed{\begin{array}{l}\rm 7)~\sf Se~a~matriz~A~possui~4~elementos\\\sf ent\tilde ao~\acute e~do~tipo~2\times2.\\\underline{\rm Matriz~gen\acute erica:}\\\sf A=\begin{bmatrix}\sf a_{11}&\sf a_{12}\\\sf a_{21}&\sf a_{22}\end{bmatrix}\\\underline{\rm c\acute alculo~dos~elementos:}\\\sf a_{11}= 1-2\cdot1=-1\\\sf a_{12}=1-2\cdot2=-3\\\sf a_{21}= 2-2\cdot1=0\\\sf a_{22}=2-2\cdot 2=-2\\\underline{\rm A~matriz~pedida~ser\acute a}\\\sf A=\begin{bmatrix}\sf-1&\sf-3\\\sf0&\sf-2\end{bmatrix}\end{array}}$