Verified answer

Resposta:

1. [tex]\begin{pmatrix}4&3&0\\ 5&3&-2\end{pmatrix}[/tex]

2. [tex]\begin{pmatrix}4&3&7\\ 7&8&-2\end{pmatrix}[/tex]

3. [tex]\begin{pmatrix}5&3&3\\ 5&5&-2\end{pmatrix}[/tex]

Explicação passo a passo:

[tex]A=\begin{pmatrix}2&3&1\\ 7&4&-2\end{pmatrix}[/tex]

[tex]B=\begin{pmatrix}-1&0&-3\\ 0&-2&0\end{pmatrix}[/tex]

[tex]C=\begin{pmatrix}-3&2\\ 0&-1\\ -2&0\end{pmatrix}[/tex]

1. [tex]A+B-C^t[/tex]

[tex]\begin{pmatrix}2&3&1\\ 7&4&-2\end{pmatrix}+\begin{pmatrix}-1&0&-3\\ 0&-2&0\end{pmatrix}-\begin{pmatrix}-3&2\\ 0&-1\\ -2&0\end{pmatrix}^t\\=\begin{pmatrix}2&3&1\\ 7&4&-2\end{pmatrix}+\begin{pmatrix}-1&0&-3\\ 0&-2&0\end{pmatrix}-\begin{pmatrix}-3&0&-2\\ 2&-1&0\end{pmatrix}\\=\begin{pmatrix}1&3&-2\\ 7&2&-2\end{pmatrix}-\begin{pmatrix}-3&0&-2\\ 2&-1&0\end{pmatrix}\\=\begin{pmatrix}4&3&0\\ 5&3&-2\end{pmatrix}[/tex]

2. [tex]A-2B[/tex]

[tex]\begin{pmatrix}2&3&1\\ 7&4&-2\end{pmatrix}-2\begin{pmatrix}-1&0&-3\\ 0&-2&0\end{pmatrix}\\=\begin{pmatrix}2&3&1\\ 7&4&-2\end{pmatrix}-\begin{pmatrix}-2&0&-6\\ 0&-4&0\end{pmatrix}\\=\begin{pmatrix}4&3&7\\ 7&8&-2\end{pmatrix}[/tex]

3. [tex]A-C^t[/tex]

[tex]\begin{pmatrix}2&3&1\\ 7&4&-2\end{pmatrix}-\begin{pmatrix}-3&2\\ 0&-1\\ -2&0\end{pmatrix}^t\\=\begin{pmatrix}2&3&1\\ 7&4&-2\end{pmatrix}-\begin{pmatrix}-3&0&-2\\ 2&-1&0\end{pmatrix}\\=\begin{pmatrix}5&3&3\\ 5&5&-2\end{pmatrix}[/tex]