Question

Sendo A.X=B, onde A= [2 −1/3 1] e B= [1 2/3 2], calcule o valor de X.​

Answer 1

$A=\left[\begin{array}{cc}2&-1\\3&1\end{array}\right]$

$B=\left[\begin{array}{cc}1&2\\3&2\end{array}\right]$

$C=\left[\begin{array}{cc}a&b\\c&d\end{array}\right]$

$\boxed{AX=B}\ \to\ \left[\begin{array}{cc}2&-1\\3&1\end{array}\right] \left[\begin{array}{cc}a&b\\c&d\end{array}\right]=\left[\begin{array}{cc}1&2\\3&2\end{array}\right] \to$

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

$\left \{ {{2a-c=1} \atop {3a+c=3}} \right.$

$(2a-c)+(3a+c)=1+3\ \to\ 5a=4\ \to\ \boxed{a=\dfrac{4}{5}}$

$2a-c=1\ \to\ c=2a-1=\dfrac{8}{5}-\dfrac{5}{5}\ \to\ \boxed{c=\dfrac{3}{5}}$

$\left \{ {{2b-d=2} \atop {3b+d=2}} \right.$

$(2b-d)+(3b+d)=2+2\ \to\ 5b=4\ \to\ \boxed{b=\dfrac{4}{5}}$

$2b-d=2\ \to\ d=2b-2=\dfrac{8}{5}-\dfrac{10}{5}\ \to\ \boxed{d=-\dfrac{2}{5}}$

$\boxed{\boxed{X=\left[\begin{array}{cc}4/5&4/5\\3/5&-2/5\end{array}\right] }}$