Question

São dadas as matrizes A=(aij) e B=(bij), quadradas de ordem 2, com aij=2i + 5j e bij=5i - 4j. considerando C=A + B, calcule a matriz C.​

Answer 1

Primeiro vamos determinar as matrizes A e B

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

$a_{ij} = 2i+5j\\\\a_{11} = 2.1+5.1 = 2+5 = 7\\a_{12} = 2.1+5.2=2 + 10 = 12\\a_{21} = 2.2+5.1=4 + 5 = 9\\a_{22} = 2.2+5.2 = 4  +10 = 14$

$A=\left[\begin{array}{cc}7 &12\\9&14\\\end{array}\right]$

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

$b_{ij} = 5i-4j\\\\b_{11} = 5.1-4.1 = 5-4 = 1\\b_{12} = 5.1-4.2=5 -8 = -3\\b_{21} = 5.2-4.1=10 -4 = 6\\b_{22} = 5.2-4.2 = 10 -8 = 2$

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

$A+B=\left[\begin{array}{cc}7 &12\\9&14\\\end{array}\right]+\left[\begin{array}{cc}1 &-3\\6&2\\\end{array}\right]\\\\C=\left[\begin{array}{cc}7+1 &12-3\\9+6&14+2\\\end{array}\right] \\\\C=\left[\begin{array}{cc}8 &9\\15&6\\\end{array}\right]$