Question

Genteeee, boa noite. Me ajudem, por favor. Preciso desses cálculos URGENTEMENTE

Answer 1

Resposta:

$\left[\begin{array}{cc}9&27\\0&36\end{array}\right]$

Explicação passo a passo:

Primeiro, descobrir quem são as matrizes A e B:

$A=\left[\begin{array}{cc}a_{11}&a_{12}\\a_{21}&a_{22}\end{array}\right]$

Se:

$a_{ij} = 2i-3j$

Então:

$\begin{cases}a_{11} = 2 - 3 = -1\\a_{12} = 2 - 6 = -4\\a_{21} = 4 - 3 = 1\\a_{22} = 4- 6 = -2\\\end{cases}$

$A=\left[\begin{array}{cc}-1&-4\\1&-2\end{array}\right]$

Para B:

$b_{ij} = \begin{cases}i + j & \text{se } i=j \\i-j & \text{se } i\neq j\end{cases}$

Então:

$\begin{cases}b_{11} = 1+1 = 2\\b_{12} = 1-2 = -1\\b_{21} = 2 - 1 = 1\\b_{22} = 2+2 = 4\\\end{cases}$

$B=\left[\begin{array}{cc}b_{11}&b_{12}\\b_{21}&b_{22}\end{array}\right] = \left[\begin{array}{cc}2&-1\\1&4\end{array}\right]$

Agora, calculando X:

$X = (B-A)$

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

$X=\left[\begin{array}{cc}2-(-1)&-1-(-4)\\1-1&4-(-2)\end{array}\right]= \left[\begin{array}{cc}3&3\\0&6\end{array}\right]$

Então, calculando X²:

$X^2 = \left[\begin{array}{cc}3&3\\0&6\end{array}\right]\cdot\left[\begin{array}{cc}3&3\\0&6\end{array}\right]=\left[\begin{array}{cc}9&27\\0&36\end{array}\right]$