Question

Dadas as matrizes A = 2 1 -3 4 e B = 8 10 1 21 -4 15 determine a matrix X tal que AX=B​

Answer 1

Resposta:

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

MULTIPLICAÇÃO DE MATRIZES

$\left[\begin{array}{ccc}2&1&\\-3&4&\\\end{array}\right] . \left[\begin{array}{ccc}a&b&c\\d&e&f\\\end{array}\right]=\left[\begin{array}{ccc}8&10&1\\21&-4&15\\\end{array}\right]$

$\left[\begin{array}{ccc} 2a+d &2b+c&2c+f\\-3a+4d&-3b+4c&-3c+4f\\\end{array}\right]=\left[\begin{array}{ccc}8&10&1\\21&-4&15\\\end{array}\right]$

Temos 3 Sistemas de Equações de 1º Grau acima:

Multiplicando por (-4) os três sistemas:

$\left \{ {{-8a - 4d = - 32} \atop {-3a+ 4d=21}} \right.$         $\left \{ {{-8b-4c=-40} \atop {-3b+4c=-4}} \right.$       $\left \{ {{-8c-4f=-4} \atop {-3c+4f=15}} \right.$

$-11a = -11$           $-11b = -44$          $- 11c = 11$

$a = -11 : -11$        $b = -44 : -11$       $c = 11 : - 11$

a = 1                       $b = 4$                    c = -1

Achando d:          Achando c:           Achando f:

$2+ d = 8\\d = 8 - 2\\d = 6$               $2.4+c = 10\\c = 10 - 8\\c = 2$           $2(-1)+f = 1\\-2 + f = 1\\f = 1 +2\\f = 3$

A matriz:  

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

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