1 Answer

Marbdq · Answer 1 · 2021-05-23T03:21:36+0000

Answer:

Let matrix
$A = \left[\begin{array}{ccc}1&2\\3&4\\\end{array}\right]$

Let matrix
$B = \left[\begin{array}{ccc}5&6\\7&8\\\end{array}\right]$

Matrix
$A^(T) = \left[\begin{array}{ccc}1&3\\2&4\\\end{array}\right]$

Matrix
$B^(T) = \left[\begin{array}{ccc}5&7\\6&8\\\end{array}\right]$

1. Solving for
(A + B)^(T)

Firstly determine (A + B), then solve
(A + B)^(T)

$A + B =\left[\begin{array}{ccc}1&2\\3&4\\\end{array}\right] + \left[\begin{array}{ccc}5&6\\7&8\\\end{array}\right]$

$A + B = \left[\begin{array}{ccc}1+5 &2+6 &\\3 + 7&4 + 8\\\end{array}\right]$

$A + B =\left[\begin{array}{ccc}6&8\\10&12\\\end{array}\right]$

$(A + B)^(T) = \left[\begin{array}{ccc}6&10\\8&12\\\end{array}\right]$ ------(1)

2. Solving for
A^(T) + B^(T)

$A^(T) + B^(T) = \left[\begin{array}{ccc}1&3\\2&4\\\end{array}\right] + \left[\begin{array}{ccc}5&7\\6&8\\\end{array}\right]$

$A^(T) + B^(T) = \left[\begin{array}{ccc}1 + 5&3 +7\\2 + 6&4+8\\\end{array}\right]$

$A^(T) + B^(T) = \left[\begin{array}{ccc}6&10\\8&12\\\end{array}\right]$ -----(2)

Comparing (1) and (2)

(A + B)^(T) = A^(T) + B^(T)

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