Question

sejam as matrizes:
A| 2 3 1
7 4 -2

B| -1 0 -3
0 -2 0

C| -3 2
0 -1
-2 0

determine:
1. A+B-C^t
2. A-2B
3. A-C^t​

Answer 1

Resposta:

1. $\begin{pmatrix}4&3&0\\ 5&3&-2\end{pmatrix}$

2. $\begin{pmatrix}4&3&7\\ 7&8&-2\end{pmatrix}$

3. $\begin{pmatrix}5&3&3\\ 5&5&-2\end{pmatrix}$

Explicação passo a passo:

$A=\begin{pmatrix}2&3&1\\ 7&4&-2\end{pmatrix}$

$B=\begin{pmatrix}-1&0&-3\\ 0&-2&0\end{pmatrix}$

$C=\begin{pmatrix}-3&2\\ 0&-1\\ -2&0\end{pmatrix}$

1. $A+B-C^t$

$\begin{pmatrix}2&3&1\\ 7&4&-2\end{pmatrix}+\begin{pmatrix}-1&0&-3\\ 0&-2&0\end{pmatrix}-\begin{pmatrix}-3&2\\ 0&-1\\ -2&0\end{pmatrix}^t\\=\begin{pmatrix}2&3&1\\ 7&4&-2\end{pmatrix}+\begin{pmatrix}-1&0&-3\\ 0&-2&0\end{pmatrix}-\begin{pmatrix}-3&0&-2\\ 2&-1&0\end{pmatrix}\\=\begin{pmatrix}1&3&-2\\ 7&2&-2\end{pmatrix}-\begin{pmatrix}-3&0&-2\\ 2&-1&0\end{pmatrix}\\=\begin{pmatrix}4&3&0\\ 5&3&-2\end{pmatrix}$

2. $A-2B$

$\begin{pmatrix}2&3&1\\ 7&4&-2\end{pmatrix}-2\begin{pmatrix}-1&0&-3\\ 0&-2&0\end{pmatrix}\\=\begin{pmatrix}2&3&1\\ 7&4&-2\end{pmatrix}-\begin{pmatrix}-2&0&-6\\ 0&-4&0\end{pmatrix}\\=\begin{pmatrix}4&3&7\\ 7&8&-2\end{pmatrix}$

3. $A-C^t$

$\begin{pmatrix}2&3&1\\ 7&4&-2\end{pmatrix}-\begin{pmatrix}-3&2\\ 0&-1\\ -2&0\end{pmatrix}^t\\=\begin{pmatrix}2&3&1\\ 7&4&-2\end{pmatrix}-\begin{pmatrix}-3&0&-2\\ 2&-1&0\end{pmatrix}\\=\begin{pmatrix}5&3&3\\ 5&5&-2\end{pmatrix}$