Question

Exercício de multiplicação de nº real por uma matriz​

Answer 1

 

$\boxed{\begin{array}{l}\bf 1)\\\sf A=\begin{pmatrix}\sf2&\sf0&\sf1\\\sf5&\sf1&\sf3\end{pmatrix}~~B=\begin{pmatrix}\sf0&\sf-1&\sf2\\\sf5&\sf0&\sf6\end{pmatrix}\\\\\tt a)~\sf 5A=5\cdot\begin{pmatrix}\sf2&\sf0&\sf1\\\sf5&\sf1&\sf3\end{pmatrix}=\begin{pmatrix}\sf10&\sf0&\sf5\\\sf25&\sf5&\sf15\end{pmatrix}\end{array}}$

$\large\boxed{\begin{array}{l}\tt b)~\sf-2B=-2\cdot\begin{pmatrix}\sf0&\sf-1&\sf2\\\sf5&\sf0&\sf6\end{pmatrix}=\begin{pmatrix}\sf0&\sf2&\sf-4\\\sf-10&\sf0&\sf-12\end{pmatrix}\end{array}}$

$\large\boxed{\begin{array}{l}\tt c)~\sf\dfrac{1}{2}A=\dfrac{1}{2}\cdot\begin{pmatrix}\sf2&\sf0&\sf1\\\sf5&\sf1&\sf3\end{pmatrix}=\begin{pmatrix}\sf1&\sf0&\sf\dfrac{1}{2}\\\\\sf\dfrac{5}{2}&\sf\dfrac{1}{2}&\sf\dfrac{3}{2}\end{pmatrix}\end{array}}$

$\large\boxed{\begin{array}{l}\tt d)~\sf2A+B=2\cdot\begin{pmatrix}\sf2&\sf0&\sf1\\\sf5&\sf1&\sf3\end{pmatrix}+3\cdot\begin{pmatrix}\sf0&\sf-1&\sf2\\\sf5&\sf0&\sf6\end{pmatrix}\\\\\sf 2A+B=\begin{pmatrix}\sf4&\sf0&\sf2\\\sf10&\sf2&\sf6\end{pmatrix}+\begin{pmatrix}\sf0&\sf-3&\sf6\\\sf15&\sf0&\sf18\end{pmatrix}\\\\\sf 2A+B=\begin{pmatrix}\sf4&\sf-3&\sf8\\\sf25&\sf2&\sf24\end{pmatrix}\end{array}}$

$\boxed{\begin{array}{l}\bf 2)\\\sf 2A+2B-4C=2\cdot\begin{pmatrix}\sf1&\sf3\\\sf2&\sf0\end{pmatrix}+2\cdot\begin{pmatrix}\sf-1&\sf3\\\sf1&\sf-2\end{pmatrix}-4\cdot\begin{pmatrix}\sf1&\sf2\\\sf4&\sf3\end{pmatrix}\\\\\sf 2A+2B-4C=\begin{pmatrix}\sf2&\sf6\\\sf4&\sf0\end{pmatrix}+\begin{pmatrix}\sf-2&\sf6\\\sf2&\sf-4\end{pmatrix}-\begin{pmatrix}\sf4&\sf8\\\sf16&\sf12\end{pmatrix}\end{array}}$

$\Large\boxed{\begin{array}{l}\sf2A+2B-4C=\begin{pmatrix}\sf2-2-4&\sf6+6+8\\\sf4+2-16&\sf0-4-12\end{pmatrix}\\\\\sf 2A+2B-4C=\begin{pmatrix}\sf-4&\sf20\\\sf-10&\sf-16\end{pmatrix}\end{array}}$