Question

dadas as matrizes A=(aij)2×2, tal que. aij={i+j, sei= j /0, sei€j e B=(bij)2x2,tal que bij= 2i-3j. calcule A+Bt.

Answer 1

Matriz A : 

$A = \left[\begin{array}{ccc}a11&a12\\a21&a22\\\end{array}\right] \\ \\ B = \left[\begin{array}{ccc}a11&a12\\a21&a22\\\end{array}\right] \\ \\ \texttt{agora vamos achar os elementos das matrizes : } \\ \\ aij = i + j ( i = j ) \\ a11 = 1 + 1 = 2 \\ a22 = 2 + 2 = 4 \\ \\ aij = 0 ( i \neq j) \\ a12 = 0 \\ a21 = 0$

$matriz : \\ \\ A = \left[\begin{array}{ccc}2&0\\0&4\\\end{array}\right]$


$\texttt{agora os elementos da matriz B: } \\ \\ bij = 2i - 3j \\ b11 = 2.1 - 3.1 = 2 - 3 = -1 \\ b12 = 2.1 - 3.2 = 2 - 6 = -4 \\ b21 = 2.2 - 3.1 = 4 - 3 = 1 \\ b22 = 2 .2 - 3.2 = 4 - 6 = -2 \\ \\ B = \left[\begin{array}{ccc}-1&-4\\1&-2\\\end{array}\right] \\ B ^{t} = \left[\begin{array}{ccc}-1&1\\-4&-2\\\end{array}\right]$

$\texttt{agora vamos fazer a soma : } \\ \\ A + B ^{t} \\ \\ \left[\begin{array}{ccc}2&0\\0&4\\\end{array}\right] + \left[\begin{array}{ccc}-1&1\\-4&2\\\end{array}\right] = \left[\begin{array}{ccc}1&1\\-4&6\\\end{array}\right]$