Question

Sendo A= [ 2 6
-1 2 ]
B= [ 3 -1
2 -2 ], Calcule B.A

ME AJUDEM POR FAVOR!!​

Answer 1

Explicação passo a passo:

A multiplicação entre matrizes é feita assim:

Sejam as matrizes genéricas de ordem 2 (2 linhas e 2 colunas)

    $A=\left[\begin{array}{ccc}a_{11}&a_{12}\\a_{21}&a_{22}\\\end{array}\right]$          $B=\left[\begin{array}{ccc}b_{11}&b_{12}\\b_{21}&b_{22}\\\end{array}\right]$          $C=\left[\begin{array}{ccc}1c_{11}&c_{12}\\c_{21}&c_{22}\\\end{array}\right]$

    $A.B=C$;     então

    $c_{11}=a_{11}.b_{11}+a_{12}.b_{21}$

    $c_{12}=a_{11}.b_{12}+a_{12}.b_{22}$

    $c_{21}=a_{21}.b_{11}+a_{22}.b_{21}$

    $c_{22}=a_{21}.b_{12}+a_{22}.b_{22}$

Então

    $B.A=\left[\begin{array}{ccc}3&-1\\2&-2\\\end{array}\right].\left[\begin{array}{ccc}2&6\\-1&2\\\end{array}\right]$

   

    $B.A=\left[\begin{array}{ccc}3.2+(-1).(-1)&3.6+(-1).2\\2.2+(-2).(-1)&2.6+(-2).2\\\end{array}\right]$

    $B.A=\left[\begin{array}{ccc}6+1&18-2\\4+2&12-4\\\end{array}\right]$

    $B.A=\left[\begin{array}{ccc}7&16\\6&8\\\end{array}\right]$