qual é a solução do sistema r+5s+t=12 r-3s+t=4 2r+s+t=15
Soluções para a tarefa
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Usando a Regra de Cramer:
![M_c= \left[\begin{array}{ccc}1&5&1\\1&-3&1\\2&1&1\end{array}\right] \\
\\
detM_C=-3+10+1+6-5-1=8\\
\\
M_r= \left[\begin{array}{ccc}12&5&1\\4&-3&1\\15&1&1\end{array}\right] \\
\\
detM_r=-36+75+4+45-20-12=56\\
\\
M_s= \left[\begin{array}{ccc}1&12&1\\1&4&1\\2&15&1\end{array}\right] \\
\\
detM_s=4+24+15-8-12-15=8\\
\\
M_t= \left[\begin{array}{ccc}1&5&12\\1&-3&4\\2&1&15\end{array}\right] \\
\\
detM_t=-45+40+12+72-75-4=0\\
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r=\frac{detM_r}{det_Mc}=\frac{56}{8}=7\\](https://tex.z-dn.net/?f=M_c%3D++%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%26amp%3B5%26amp%3B1%5C%5C1%26amp%3B-3%26amp%3B1%5C%5C2%26amp%3B1%26amp%3B1%5Cend%7Barray%7D%5Cright%5D+%5C%5C%0A%5C%5C%0AdetM_C%3D-3%2B10%2B1%2B6-5-1%3D8%5C%5C%0A%5C%5C%0AM_r%3D++%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D12%26amp%3B5%26amp%3B1%5C%5C4%26amp%3B-3%26amp%3B1%5C%5C15%26amp%3B1%26amp%3B1%5Cend%7Barray%7D%5Cright%5D+%5C%5C%0A%5C%5C%0AdetM_r%3D-36%2B75%2B4%2B45-20-12%3D56%5C%5C%0A%5C%5C%0AM_s%3D++%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%26amp%3B12%26amp%3B1%5C%5C1%26amp%3B4%26amp%3B1%5C%5C2%26amp%3B15%26amp%3B1%5Cend%7Barray%7D%5Cright%5D+%5C%5C%0A%5C%5C%0AdetM_s%3D4%2B24%2B15-8-12-15%3D8%5C%5C%0A%5C%5C%0AM_t%3D++%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%26amp%3B5%26amp%3B12%5C%5C1%26amp%3B-3%26amp%3B4%5C%5C2%26amp%3B1%26amp%3B15%5Cend%7Barray%7D%5Cright%5D+%5C%5C%0A%5C%5C%0AdetM_t%3D-45%2B40%2B12%2B72-75-4%3D0%5C%5C%0A%5C%5C%0Ar%3D%5Cfrac%7BdetM_r%7D%7Bdet_Mc%7D%3D%5Cfrac%7B56%7D%7B8%7D%3D7%5C%5C%0A%0A%0A%0A "M_c= \left[\begin{array}{ccc}1&5&1\\1&-3&1\\2&1&1\end{array}\right] \\
\\
detM_C=-3+10+1+6-5-1=8\\
\\
M_r= \left[\begin{array}{ccc}12&5&1\\4&-3&1\\15&1&1\end{array}\right] \\
\\
detM_r=-36+75+4+45-20-12=56\\
\\
M_s= \left[\begin{array}{ccc}1&12&1\\1&4&1\\2&15&1\end{array}\right] \\
\\
detM_s=4+24+15-8-12-15=8\\
\\
M_t= \left[\begin{array}{ccc}1&5&12\\1&-3&4\\2&1&15\end{array}\right] \\
\\
detM_t=-45+40+12+72-75-4=0\\
\\
r=\frac{detM_r}{det_Mc}=\frac{56}{8}=7\\")
S={(7,1,0)}
S={(7,1,0)}
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