Sendo A=|2 1| , qual a solucao da equação x+5A=A²+2I₂
|1 3| ⇒ isso é uma matriz
ivanoliveira96:
em 2I..... o I é a matriz identidade
Soluções para a tarefa
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Olá, Ivan.
![X+5A=A\²+2I_2\Rightarrow\\\\
X+5 \left[\begin{array}{cc} 2&1\\1&3\end{array}\right] =\left[\begin{array}{cc} 2&1\\1&3\end{array}\right] \cdot\left[\begin{array}{cc} 2&1\\1&3\end{array}\right] +2\left[\begin{array}{cc} 1&0\\0&1\end{array}\right] \Rightarrow\\\\
X+\left[\begin{array}{cc} 10&5\\5&15\end{array}\right] =\left[\begin{array}{cc} 5&5\\5&10\end{array}\right]+\left[\begin{array}{cc} 2&0\\0&2\end{array}\right] \Rightarrow](https://tex.z-dn.net/?f=X%2B5A%3DA%5C%C2%B2%2B2I_2%5CRightarrow%5C%5C%5C%5C%0AX%2B5++%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D+2%26amp%3B1%5C%5C1%26amp%3B3%5Cend%7Barray%7D%5Cright%5D+%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D+2%26amp%3B1%5C%5C1%26amp%3B3%5Cend%7Barray%7D%5Cright%5D+%5Ccdot%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D+2%26amp%3B1%5C%5C1%26amp%3B3%5Cend%7Barray%7D%5Cright%5D+%2B2%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D+1%26amp%3B0%5C%5C0%26amp%3B1%5Cend%7Barray%7D%5Cright%5D+%5CRightarrow%5C%5C%5C%5C%0AX%2B%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D+10%26amp%3B5%5C%5C5%26amp%3B15%5Cend%7Barray%7D%5Cright%5D+%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D+5%26amp%3B5%5C%5C5%26amp%3B10%5Cend%7Barray%7D%5Cright%5D%2B%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D+2%26amp%3B0%5C%5C0%26amp%3B2%5Cend%7Barray%7D%5Cright%5D+%5CRightarrow "X+5A=A\²+2I_2\Rightarrow\\\\
X+5 \left[\begin{array}{cc} 2&1\\1&3\end{array}\right] =\left[\begin{array}{cc} 2&1\\1&3\end{array}\right] \cdot\left[\begin{array}{cc} 2&1\\1&3\end{array}\right] +2\left[\begin{array}{cc} 1&0\\0&1\end{array}\right] \Rightarrow\\\\
X+\left[\begin{array}{cc} 10&5\\5&15\end{array}\right] =\left[\begin{array}{cc} 5&5\\5&10\end{array}\right]+\left[\begin{array}{cc} 2&0\\0&2\end{array}\right] \Rightarrow")
![X=\left[\begin{array}{cc} 7&5\\5&12\end{array}\right]-\left[\begin{array}{cc} 10&5\\5&15\end{array}\right] \Rightarrow\\\\
X=\left[\begin{array}{cc} -3&0\\0&-3\end{array}\right]\Rightarrow\\\\
\boxed{X=-3I_2}](https://tex.z-dn.net/?f=X%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D+7%26amp%3B5%5C%5C5%26amp%3B12%5Cend%7Barray%7D%5Cright%5D-%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D+10%26amp%3B5%5C%5C5%26amp%3B15%5Cend%7Barray%7D%5Cright%5D++%5CRightarrow%5C%5C%5C%5C%0AX%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D+-3%26amp%3B0%5C%5C0%26amp%3B-3%5Cend%7Barray%7D%5Cright%5D%5CRightarrow%5C%5C%5C%5C%0A%5Cboxed%7BX%3D-3I_2%7D "X=\left[\begin{array}{cc} 7&5\\5&12\end{array}\right]-\left[\begin{array}{cc} 10&5\\5&15\end{array}\right] \Rightarrow\\\\
X=\left[\begin{array}{cc} -3&0\\0&-3\end{array}\right]\Rightarrow\\\\
\boxed{X=-3I_2}")
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