Question

Resolva a equação matricial A·X = B, sendo A=$\left[\begin{array}{ccc}2&-1\\-3&2\\\end{array}\right]$
B=$\left[\begin{array}{ccc}3&1\\2&1\\\end{array}\right]$

R: $\left[\begin{array}{ccc}8&3\\13&5\\\end{array}\right]$

Answer 1

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

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

Multiplicando a primeira equação por 2:

$\left \{ {{4a-2c=6} \atop {-3a+2c=2}} \right.$

Somando as equações:

$4a-3a-2c+2c=6+2\\a=8$

$2a-c=3\\c=2a-3\\c=2*8-3\\c=16-3\\c=13$

Resolvendo o outro sistema:

$\left \{ {{2b-d=1} \atop {-3b+2d=1}} \right.$

Multiplicando a primeira equação por 2:

$\left \{ {{4b-2d=2} \atop {-3b+2d=1}} \right.$

Somando as equações:

$4b-3b-2d+2d=2+1\\b=3$

$2b-d=1\\d=2b-1\\d=2*3-1\\d=6-1\\d=5$
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$X=\left[\begin{array}{cc}a&b\\c&d\end{array}\right]\\\\X=\left[\begin{array}{cc}8&3\\13&5\end{array}\right]$