Question

me ajuda nessa questão !!!​

Answer 1

Moço sempre qnd for fechar matriz fecha com colchetes pq se for só linha pode confundir com determinantes e a C não tem como multiplicar pq as colunas da matriz A tem q ser o mesmo número de linhas da outra matriz que vai ser multiplicada, se está com duvida nesse conteúdo recomendo demais ver esse vídeo do sandro carió https://youtu.be/KKCmjnU2y3o

Answer 2

Resposta:

$a)\ A\times B=\left[\begin{array}{ccc}-16&20&4\\-13&15&0\end{array}\right]$

$b)\ B\times C=\left[\begin{array}{c}17\\-10\end{array}\right]$

$c)\ A\times C\ \ \Rightarrow\ \ N\~ao\ e\´\ possi\´vel\ haver\ multiplica\c c\~ao.$

Explicação passo a passo:

$A=\left[\begin{array}{cc}4&0\\3&-1\end{array}\right]$   $B=\left[\begin{array}{ccc}-4&5&1\\1&0&3\end{array}\right]$    $C=\left[\begin{array}{c}8\\11\\-6\end{array}\right]$

$a)\ A\times B\\\\\left[\begin{array}{cc}4&0\\3&-1\end{array}\right] \times\left[\begin{array}{ccc}-4&5&1\\1&0&3\end{array}\right] \\\\\\(AB)_{11} = 4\times(-4)+0\times1\\\\(AB)_{11} =(-16)+0\\\\(AB)_{11} =(-16)\\\\\\(AB)_{12} =4\times5+0\times0\\\\(AB)_{12} =20+0\\\\(AB)_{12} =20\\\\\\(AB)_{13} =4\times1+0\times3\\\\(AB)_{13} =4+0\\\\(AB)_{13} =4\\\\\\(AB)_{21} =3\times(-4)+(-1)\times1\\\\(AB)_{21} =(-12)-1\\\\(AB)_{21} =(-13)$

$(AB)_{22} =3\times5+(-1)\times0\\\\(AB)_{22} =15-0\\\\(AB)_{22} =15\\\\\\(AB)_{23} =3\times1+(-1)\times3\\\\(AB)_{23} =3-3\\\\(AB)_{23} =0$

$A\times B=\left[\begin{array}{ccc}-16&20&4\\-13&15&0\end{array}\right]$

$b)\ B\times C\\\\\left[\begin{array}{ccc}-4&5&1\\1&0&3\end{array}\right] \times \left[\begin{array}{c}8\\11\\-6\end{array}\right] \\\\\\(BC)_{11} = (-4)\times8+5\times11+1\times(-6)\\\\(BC)_{11} = (-32)+55-6\\\\(BC)_{11} = 23-6\\\\(BC)_{11} = 17\\\\\\(BC)_{21} = 1\times8+0\times11+3\times(-6)\\\\(BC)_{21} = 8+0-18\\\\(BC)_{21} = 8-18\\\\(BC)_{21} = (-10)$

$B\times C=\left[\begin{array}{c}17\\-10\end{array}\right]$

$c)\ A\times C\\\\Como\ em\ (A_{2\bold{2}}\ e\ C_{\bold{3}1} )\ o\ nu\´mero\ de\ colunas\ de\ \bold{A}\ e\´\ diferente\ do\ n\´umero\ de\ linhas\ de\ \bold{C},$

$portanto\ n\~ao\ e\´\ possi\´vel\ haver\ multiplica\c c\~ao.$