Question

Dada a matriz: $\left[\begin{array}{ccc}1&4&10\\-2&-1&1\\3&5&2\end{array}\right]$ calcule:
a) X= A+A^t
b) Y=A^t-A
R= $\left[\begin{array}{ccc}2&2&3\\2&-2&6\\3&6&4\end{array}\right]$
e Y= $\left[\begin{array}{ccc}0&-6&3\\6&0&4\\-3&-4&0\end{array}\right]$

Answer 1

$Ola' \\ \\ a)~x=A+ A^{t} ~~--\ \textgreater \ lembre~~ A^{t}=\begin{vmatrix}1&-2&3 \\ 4&-1&5 \\ 10&1&2\end{vmatrix}_{3_X3} \\ \\ x=\begin{vmatrix}1&4&10 \\ -2&-1&1 \\ 3&5&2\end{vmatrix}+\begin{vmatrix}1&-2&3 \\ 4&-1&5 \\ 10&1&2\end{vmatrix} \\ \\ \\ x=\begin{vmatrix}1-2&4-2&10+3 \\ -2+4&-1-1&1+5 \\ 3+10&5+1&2+2\end{vmatrix} \\ \\ \\\boxed{ x=\begin{vmatrix}-1&2&13 \\ 2&-2&6 \\ 13&6&4\end{vmatrix}_{3_X3}}$

$\mathbb{ttttttttttttttttttttttttttttttttttttttt} \\ b) ~y= A^{t}-A \\ \\ y=\begin{vmatrix}1&-2&3 \\ 4&-1&5 \\ 10&1&2\end{vmatrix}-\begin{vmatrix}1&4&10 \\ -2&-1&1 \\ 3&5&2\end{vmatrix} \\ \\ \\ y=\begin{vmatrix}1-1&-2-4&3-10 \\ 4-(-2)&-1-(-1)&5-1 \\ 10-3&1-5&2-2\end{vmatrix} \\ \\ \\ \boxed{y=\begin{vmatrix}0&-6&-7 \\ 6&0&4 \\ 7&-4&0\end{vmatrix}_{3_X3}}$

$\mathbb{iiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii} \\~~~~~~~~~~~~~~~~~~~~~~~~~~Espero~ter~ajudado!!$