Question

1 - Considere as matrizes
A = ( Aij) e B ( bij ), quadradas de ordem 3 com Aij = 3i + 4j e bij = - 4i -3j, Sabendo que C=A+B ,determine C2 ao quadrado

Answer 1

$\begin{matrix}A=(a_{ij})_{3\times3}}\\\\a_{ij}=3i+4j\end{matrix}\qquad\qquad\qquad\qquad\begin{matrix}B=(b_{ij})_{3\times3}}\\\\b_{ij}=-4i-3j\\\end{matrix}\\\\\\\\C=A+B\Leftrightarrow c_{ij}=a_{ij}+b_{ij}\\\\c_{ij}=(3i+4j)+(-4i-3j)\to c_{ij}=-i+j$



$\\\\\\c_{11}=-(1)+(1)\to c_{11}=0\\\\c_{12}=-(1)+(2)\to c_{12}=1\\\\c_{13}=-(1)+(3)\to c_{13}=2\\\\c_{21}=-(2)+(1)\to c_{21}=-1\\\\c_{22}=-(2)+(2)\to c_{22}=0\\\\c_{23}=-(2)+(3)\to c_{23}=1\\\\c_{31}=-(3)+(1)\to c_{31}=-2\\\\c_{32}=-(3)+(2)\to c_{32}=-1\\\\c_{33}=-(3)+(3)\to c_{33}=0$



$C=\left[\begin{array}{ccc}c_{11}&c_{12}&c_{13}\\c_{21}&c_{22}&c_{23}\\c_{31}&c_{32}&c_{33}\end{array}\right]\to C=\left[\begin{array}{ccc}0&1&2\\-1&0&1\\-2&-1&0\end{array}\right]\\\\\\\\C^2=\left[\begin{array}{ccc}0&1&2\\-1&0&1\\-2&-1&0\end{array}\right]\cdot\left[\begin{array}{ccc}0&1&2\\-1&0&1\\-2&-1&0\end{array}\right]\\\\\\\\C^2=\left[\begin{array}{ccc}(0\cdot0+1\cdot-1+2\cdot-2)&(0\cdot1+1\cdot0+2\cdot-1)&(0\cdot2+1\cdot1+2\cdot0)\\{(}-1\cdot0+0\cdot-1+1\cdot-2)&(-1\cdot1+0\cdot0+1\cdot-1)&(-1\cdot2+0\cdot1+1\cdot0)\\{(}-2\cdot0+-1\cdot-1+0\cdot-2)&(-2\cdot1+-1\cdot0+0\cdot-1)&(-2\cdot2+-1\cdot1+0\cdot0)\end{array}\right]$


$C^2=\left[\begin{array}{ccc}-5&-2&1\\-2&-2&-2\\1&-2&-5\end{array}\right]$





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