Question

Me ajudammmmmmm resolve a equações matricial ​

Answer 1

Resposta:

a)

$\left[\begin{array}{ccc}a&b\\c&d\end{array}\right]*\left[\begin{array}{ccc}2&3\\1&0\end{array}\right] =\left[\begin{array}{ccc}3&6\\2&9\end{array}\right]\\\\\\\left[\begin{array}{ccc}2a+b&3a\\2c+d&3c\end{array}\right] \left[\begin{array}{ccc}3&6\\2&9\end{array}\right]\\\\\\ Comparando c\'elula com c\'elula \\3a=6 \Rightarrow a=2\\3c=9 \Rightarrow c=3\\2a+b=3 \Rightarrow 2(2)+b=3\Rightarrow b=-1\\2c+d=2\Rightarrow 2(3)+d=2\Rightarrow d=-4$

$\left[\begin{array}{ccc}a&b\\c&d\end{array}\right]=\left[\begin{array}{ccc}2&-1\\3&-4\end{array}\right]$

b)

$\left[\begin{array}{ccc}2&3&1\\4&-2&0\\2&0&0\end{array}\right] *\left[\begin{array}{ccc}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}1\\4\\6\end{array}\right]\\\\ Vamos resolver utilizando a Regra de Cramer \\determinante (D)=\left[\begin{array}{ccc}2&3&1\\4&-2&0\\2&0&0\end{array}\right] =0+0+0-(-4)=4\\\\\\determinante (Dx)=\left[\begin{array}{ccc}1&3&1\\4&-2&0\\6&0&0\end{array}\right] =0+0+0-(-12)-0-0=12$

$determinante (Dy)=\left[\begin{array}{ccc}2&1&1\\4&4&0\\2&6&0\end{array}\right]=0+0+24-8-0-0=16\\\\\\determinante (Dz)=\left[\begin{array}{ccc}2&3&1\\4&-2&4\\2&0&6\end{array}\right]=-24+24+0-(-4)-72-0=-68\\\\\\ x=\frac{Dx}{D}=\frac{12}{4}=3\\ y=\frac{Dy}{D}=\frac{16}{4}=4\\\\ z=\frac{Dz}{D}=-\frac{68}{4}=-17$

$\left[\begin{array}{ccc}2&3&1\\4&-2&0\\2&0&0\end{array}\right] *\left[\begin{array}{ccc}3\\4\\-17\end{array}\right] =\left[\begin{array}{ccc}1\\4\\6\end{array}\right]$