Question

Resolva as operações abaixo, utilizando as matrizes abaixo:

Answer 1

Explicação passo-a-passo:

$A=(a_{ij}) _{3.3}$  →  matriz de ordem 3

                                             $A=\left[\begin{array}{ccc}a_{11}&a_{12}&a_{13}\\a_{21} &a_{22} &a_{23} \\a_{31} &a_{32} &a_{33}\end{array}\right]$

    $a_{11}$ → $1=1$ → $a_{11}=10$

    $a_{12}$ → $1\neq2$ → $a_{12}=0$

    $a_{13}$ → $1\neq3$ → $a_{13}=0$

    $a_{21}$ → $2\neq1$ → $a_{21}=0$

    $a_{22}$ → $2=2$ → $a_{22}=10$

    $a_{23}$ → $2\neq3$ → $a_{23}=0$

    $a_{31}$ → $3\neq1$ → $a_{31}=0$

    $a_{32}$ → $3\neq2$ → $a_{32}=0$

    $a_{33}$ → $3=3$ → $a_{33}=10$

Daí:

                                             $A=\left[\begin{array}{ccc}10&0&0\\0&10&0\\0&0&10\end{array}\right]$

temos uma matriz diagonal

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$B=(b_{ij}) _{3.3}$  →  matriz de ordem 3

                                             $B=\left[\begin{array}{ccc}b_{11}&b_{12}&b_{13}\\b_{21}&b_{22}&b_{23}\\b_{31} &b_{32}&b_{33}\end{array}\right]$

    $b_{11}$ → $1=1$ → $b_{11}=3$

    $b_{12}$ → $1\neq2$ → $b_{12}=0$

    $b_{13}$ → $1\neq3$ → $b_{13}=0$

    $b_{21}$ → $2\neq1$ → $b_{21}=0$

    $b_{22}$ → $2=2$ → $b_{22}=3$

    $b_{23}$ → $2\neq3$ → $b_{23}=0$

    $b_{31}$ → $3\neq1$ → $b_{31}=0$

    $b_{32}$ → $3\neq2$ → $b_{32}=0$

    $b_{33}$ → $3=3$ → $b_{33}=3$

Daí:

                                             $B=\left[\begin{array}{ccc}3&0&0\\0&3&0\\0&0&3\end{array}\right]$

temos uma matriz diagonal

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Cálculo de A . B

    $A.B=\left[\begin{array}{ccc}10&0&0\\0&10&0\\0&0&10\end{array}\right].\left[\begin{array}{ccc}3&0&0\\0&3&0\\0&0&3\end{array}\right]$

    $A.B=\left[\begin{array}{ccc}10.3+0.0+0.0&10.0+0.3+0.0&10.0+0.0+0.3\\0.3+10.0+0.0&0.0+10.3+0.0&0.0+10.0+0.3\\0.3+0.0+10.0&0.0+0.3+10.0&0.0+0.1+10.3\end{array}\right]$

    $A.B=\left[\begin{array}{ccc}30+0+0&0+0+0&0+0+0\\0+0+0&0+30+0&0+0+0\\0+0+0&0+0+0&0+0+30\end{array}\right]$

    $A.B=\left[\begin{array}{ccc}30&0&0\\0&30&0\\0&0&30\end{array}\right]$

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Cálculo de  det (A.B)

    $det(A.B)=\left[\begin{array}{ccc}30&0&0\\0&30&0\\0&0&30\end{array}\right]\left[\begin{array}{ccc}30&0\\0&30\\0&0\end{array}\right]$

    det(A.B) = 30×30×30+0×0×0+0×0×0-0×30×0-30×0×0-0×0×30

    det(A.B) = 27000+0+0-0-0-0

    det(A.B) = 27000