Question

me ajuda ai por favor

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Answer 1

Resposta:

Explicação passo a passo:

$c=\begin{pmatrix}1&0&2\\ 3&5&4\\ 2&1&0\end{pmatrix}+\begin{pmatrix}0&1&3\\ 4&2&5\\ 0&2&1\end{pmatrix}\\\\\\=\begin{pmatrix}1+0&0+1&2+3\\ 3+4&5+2&4+5\\ 2+0&1+2&0+1\end{pmatrix}\\\\\\=\begin{pmatrix}1&1&5\\ 7&7&9\\ 2&3&1\end{pmatrix}$          $d=\begin{pmatrix}1&0&2\\ 3&5&4\\ 2&1&0\end{pmatrix}-\begin{pmatrix}0&1&3\\ 4&2&5\\ 0&2&1\end{pmatrix}\\\\\\=\begin{pmatrix}1-0&0-1&2-3\\ 3-4&5-2&4-5\\ 2-0&1-2&0-1\end{pmatrix}\\\\\\=\begin{pmatrix}1&-1&-1\\ -1&3&-1\\ 2&-1&-1\end{pmatrix}$

$e=\begin{pmatrix}1&0&2\\ \:\:\:3&5&4\\ \:\:\:2&1&0\end{pmatrix}\cdot \begin{pmatrix}0&1&3\\ \:\:\:4&2&5\\ \:\:\:0&2&1\end{pmatrix}\\\\=\begin{pmatrix}1\cdot \:0+0\cdot \:4+2\cdot \:0&1\cdot \:1+0\cdot \:2+2\cdot \:2&1\cdot \:3+0\cdot \:5+2\cdot \:1\\ 3\cdot \:0+5\cdot \:4+4\cdot \:0&3\cdot \:1+5\cdot \:2+4\cdot \:2&3\cdot \:3+5\cdot \:5+4\cdot \:1\\ 2\cdot \:0+1\cdot \:4+0\cdot \:0&2\cdot \:1+1\cdot \:2+0\cdot \:2&2\cdot \:3+1\cdot \:5+0\cdot \:1\end{pmatrix}$

$=\begin{pmatrix}0&5&5\\ 20&21&38\\ 4&4&11\end{pmatrix}$

$f=1\cdot \begin{pmatrix}1&0&2\\ 3&5&4\\ 2&1&0\end{pmatrix}=\begin{pmatrix}1&0&2\\ 3&5&4\\ 2&1&0\end{pmatrix}$

$g=2\begin{pmatrix}0&1&3\\ 4&2&5\\ 0&2&1\end{pmatrix}=\begin{pmatrix}2\cdot \:0&2\cdot \:1&2\cdot \:3\\ 2\cdot \:4&2\cdot \:2&2\cdot \:5\\ 2\cdot \:0&2\cdot \:2&2\cdot \:1\end{pmatrix}=\begin{pmatrix}0&2&6\\ 8&4&10\\ 0&4&2\end{pmatrix}$

2)

$\det \begin{pmatrix}a\:&\:b\:\\ c\:&\:d\:\end{pmatrix}\:=\:ad-bc\\\\\det \begin{pmatrix}x&2\\ 3&4\end{pmatrix}=4x-6\\\\4x-6=10\\4x=16\\x=4$

3)

$\begin{pmatrix}3&27&9\\ \:9&3&3\\ \:27&9&3\end{pmatrix}=3\cdot \:y\\\\\det \begin{pmatrix}3&27&9\\ 9&3&3\\ 27&9&3\end{pmatrix}\\\\=3\cdot \det \begin{pmatrix}3&3\\ 9&3\end{pmatrix}-27\cdot \det \begin{pmatrix}9&3\\ 27&3\end{pmatrix}+9\cdot \det \begin{pmatrix}9&3\\ 27&9\end{pmatrix}\\\\=3\left(-18\right)-27\left(-54\right)+9\cdot \:0\\\\=1404\\1404=3y\\y=468$