Question

Caso seja possivel encronte os produtos de AB e BA.

me ajudem obrigado.

Answer 1

Resposta:

Explicação passo a passo:

$a)$

$AB=\left[\begin{array}{ccc}0&1\\2&3\\\end{array}\right] \:.\:\left[\begin{array}{ccc}1&-1\\5&2\\\end{array}\right] =\left[\begin{array}{ccc}0.1+1.5&0.(-1)+1.2\\2.1+3.5&2.(-1)+3.2\\\end{array}\right] =\left[\begin{array}{ccc}5&2\\17&4\\\end{array}\right]$

$BA=\left[\begin{array}{ccc}1&-1\\5&2\\\end{array}\right] \:.\:\left[\begin{array}{ccc}0&1\\2&3\\\end{array}\right]=\left[\begin{array}{ccc}1.0+(-1).2&1.1+(-1).3\\5.0+2.2&5.1+2.3\\\end{array}\right] =\left[\begin{array}{ccc}-2&-2\\4&11\\\end{array}\right]$

$b)$

$AB=\left[\begin{array}{ccc}1&-1\\5&2\\\end{array}\right] \:.\:\left[\begin{array}{ccc}1&-1&5\\0&1&9\\\end{array}\right] =\left[\begin{array}{ccc}1.1+(-1).0&1.(-1)+(-1).1&1.5+(-1).9\\5.1+2.0&5.(-1)+2.1&5.5+2.9\\\end{array}\right] =$$AB=\left[\begin{array}{ccc}1&-2&-4\\5&-3&43\\\end{array}\right]$

$BA=>(nao\:e\;possivel)!$

$c)$

$AB=\left[\begin{array}{cccc}3&2&1&6\\\end{array}\right] \:.\:\left[\begin{array}{c}5&2&0\\1\end{array}\right] =\left[\begin{array}{c}3.5+2.2+1.0+6.1\end{array}\right] =\left[\begin{array}{c}15+4+0+6\end{array}\right] =\left[\begin{array}{c}25\end{array}\right]$

$BA=\left[\begin{array}{}5&2&0\\1\end{array}\right] \:.\:\left[\begin{array}{cccc}3&2&1&6\\\end{array}\right] =\left[\begin{array}{cccc}5.3&5.2&5.1&5.6\\2.3&2.2&2.1&2.6&0.3&0.2&0.1&0.6\\1.3&1.2&1.1&1.6\end{array}\right] =$

$\left[\begin{array}{cccc}15&10&5&30\\6&4&2&12\\0&0&0&0&3&2&1&6\end{array}\right]$