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A) Construir a matriz B.
![B = \left[\begin{array}{ccc}a11&a12&a13\\a21&22&a23\\a31&a32&a33\end{array}\right]](https://tex.z-dn.net/?f=B+%3D+%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Da11%26amp%3Ba12%26amp%3Ba13%5C%5Ca21%26amp%3B22%26amp%3Ba23%5C%5Ca31%26amp%3Ba32%26amp%3Ba33%5Cend%7Barray%7D%5Cright%5D "B = \left[\begin{array}{ccc}a11&a12&a13\\a21&22&a23\\a31&a32&a33\end{array}\right]")
![B = \left[\begin{array}{ccc}1^{3} &0&0\\2^{3}&2^{3}&0\\3^{3}&3^{3}&3^{3}\end{array}\right]](https://tex.z-dn.net/?f=+B+%3D+%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%5E%7B3%7D+%26amp%3B0%26amp%3B0%5C%5C2%5E%7B3%7D%26amp%3B2%5E%7B3%7D%26amp%3B0%5C%5C3%5E%7B3%7D%26amp%3B3%5E%7B3%7D%26amp%3B3%5E%7B3%7D%5Cend%7Barray%7D%5Cright%5D+ "B = \left[\begin{array}{ccc}1^{3} &0&0\\2^{3}&2^{3}&0\\3^{3}&3^{3}&3^{3}\end{array}\right]")
![B = \left[\begin{array}{ccc}1&0&0\\8&8&0\\27&27&27\end{array}\right]](https://tex.z-dn.net/?f=B+%3D+%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%26amp%3B0%26amp%3B0%5C%5C8%26amp%3B8%26amp%3B0%5C%5C27%26amp%3B27%26amp%3B27%5Cend%7Barray%7D%5Cright%5D "B = \left[\begin{array}{ccc}1&0&0\\8&8&0\\27&27&27\end{array}\right]")
B) Achar os valores de a, b, c e d
![\left[\begin{array}{ccc}a + b&b+c\\2b&2a-3d\end{array}\right] = \left[\begin{array}{ccc}9&-1\\6&18\end{array}\right] \\ \\ a+b = 9 \\ b+c = -1 \\ 2b = 6 \\ 2b-3d = 18 \\ \\ b = 6/2 \\ b = 3 \\ \\ a + 3 = 9 \\ a = 9-3 \\ a = 6 \\ \\ 3 + c = -1 \\ c = 3-1 \\ c = 2 \\ \\ 2*3 - 3d = 18 \\ -3d = 12 \\ d = -12/3 \\ d = -4](https://tex.z-dn.net/?f=++%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Da+%2B+b%26amp%3Bb%2Bc%5C%5C2b%26amp%3B2a-3d%5Cend%7Barray%7D%5Cright%5D+%3D+++%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D9%26amp%3B-1%5C%5C6%26amp%3B18%5Cend%7Barray%7D%5Cright%5D+%5C%5C++%5C%5C+a%2Bb+%3D+9++%5C%5C++b%2Bc+%3D+-1++%5C%5C++2b+%3D+6++%5C%5C+2b-3d+%3D+18++%5C%5C++%5C%5C++b+%3D+6%2F2++%5C%5C++b+%3D+3++%5C%5C+++%5C%5C++a+%2B+3+%3D+9++%5C%5C+a+%3D+9-3+%5C%5C+a+%3D+6++%5C%5C++%5C%5C++3+%2B+c+%3D+-1+%5C%5C+c+%3D+3-1++%5C%5C++c+%3D+2++%5C%5C++%5C%5C+2%2A3+-+3d+%3D+18+%5C%5C+-3d+%3D+12++%5C%5C++d+%3D+-12%2F3++%5C%5C++d+%3D+-4++ "\left[\begin{array}{ccc}a + b&b+c\\2b&2a-3d\end{array}\right] = \left[\begin{array}{ccc}9&-1\\6&18\end{array}\right] \\ \\ a+b = 9 \\ b+c = -1 \\ 2b = 6 \\ 2b-3d = 18 \\ \\ b = 6/2 \\ b = 3 \\ \\ a + 3 = 9 \\ a = 9-3 \\ a = 6 \\ \\ 3 + c = -1 \\ c = 3-1 \\ c = 2 \\ \\ 2*3 - 3d = 18 \\ -3d = 12 \\ d = -12/3 \\ d = -4")
C) A = aij // aij = 2i - 3j // X + 2A = B
![\left[\begin{array}{ccc}a11&a12\\a21&a22\end{array}\right]](https://tex.z-dn.net/?f=++%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Da11%26amp%3Ba12%5C%5Ca21%26amp%3Ba22%5Cend%7Barray%7D%5Cright%5D+ "\left[\begin{array}{ccc}a11&a12\\a21&a22\end{array}\right]")
![A = \left[\begin{array}{ccc}2*1 - 3*1&2*1 - 3*2\\2*2 - 3*1&2*2 - 3*2\end{array}\right] \\
A = \left[\begin{array}{ccc}2 - 3&2 - 6\\4 - 3&4 - 6\end{array}\right] \\
A =\left[\begin{array}{ccc}-1&-4\\1&-2\end{array}\right]
\\ \\
2A = 2*\left[\begin{array}{ccc}-1&-4\\1&-2\end{array}\right]
\\
2A = \left[\begin{array}{ccc}-2&-8\\2&-4\end{array}\right]
\\
X + \left[\begin{array}{ccc}-2&-8\\2&-4\end{array}\right] = \left[\begin{array}{ccc}1&0\\-1&1\end{array}\right] \\](https://tex.z-dn.net/?f=A+%3D+%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%2A1+-+3%2A1%26amp%3B2%2A1+-+3%2A2%5C%5C2%2A2+-+3%2A1%26amp%3B2%2A2+-+3%2A2%5Cend%7Barray%7D%5Cright%5D++%5C%5C++%0AA+%3D+%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2+-+3%26amp%3B2+-+6%5C%5C4+-+3%26amp%3B4+-+6%5Cend%7Barray%7D%5Cright%5D++%5C%5C++%0AA+%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-1%26amp%3B-4%5C%5C1%26amp%3B-2%5Cend%7Barray%7D%5Cright%5D%0A+%5C%5C++%5C%5C+%0A2A+%3D+2%2A%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-1%26amp%3B-4%5C%5C1%26amp%3B-2%5Cend%7Barray%7D%5Cright%5D%0A+%5C%5C+%0A2A+%3D+%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-2%26amp%3B-8%5C%5C2%26amp%3B-4%5Cend%7Barray%7D%5Cright%5D%0A+%5C%5C+%0AX+%2B+%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-2%26amp%3B-8%5C%5C2%26amp%3B-4%5Cend%7Barray%7D%5Cright%5D+%3D+%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%26amp%3B0%5C%5C-1%26amp%3B1%5Cend%7Barray%7D%5Cright%5D++%5C%5C+%0A "A = \left[\begin{array}{ccc}2*1 - 3*1&2*1 - 3*2\\2*2 - 3*1&2*2 - 3*2\end{array}\right] \\
A = \left[\begin{array}{ccc}2 - 3&2 - 6\\4 - 3&4 - 6\end{array}\right] \\
A =\left[\begin{array}{ccc}-1&-4\\1&-2\end{array}\right]
\\ \\
2A = 2*\left[\begin{array}{ccc}-1&-4\\1&-2\end{array}\right]
\\
2A = \left[\begin{array}{ccc}-2&-8\\2&-4\end{array}\right]
\\
X + \left[\begin{array}{ccc}-2&-8\\2&-4\end{array}\right] = \left[\begin{array}{ccc}1&0\\-1&1\end{array}\right] \\")
![X = \left[\begin{array}{ccc}1&0\\-1&1\end{array}\right] - \left[\begin{array}{ccc}-2&-8\\2&-4\end{array}\right] \\
X = \left[\begin{array}{ccc}1-(-2)&0 -(-8)\\-1 - 2&1 -(-4)\end{array}\right] \\
X = \left[\begin{array}{ccc}1+2&8\\-3&1+4\end{array}\right] \\
X = \left[\begin{array}{ccc}3&8\\-3&5\end{array}\right]](https://tex.z-dn.net/?f=X+%3D+%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%26amp%3B0%5C%5C-1%26amp%3B1%5Cend%7Barray%7D%5Cright%5D+-+%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-2%26amp%3B-8%5C%5C2%26amp%3B-4%5Cend%7Barray%7D%5Cright%5D++%5C%5C+%0AX+%3D+%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1-%28-2%29%26amp%3B0+-%28-8%29%5C%5C-1+-+2%26amp%3B1+-%28-4%29%5Cend%7Barray%7D%5Cright%5D++%5C%5C+%0AX+%3D+%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%2B2%26amp%3B8%5C%5C-3%26amp%3B1%2B4%5Cend%7Barray%7D%5Cright%5D+%5C%5C+%0AX+%3D+%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D3%26amp%3B8%5C%5C-3%26amp%3B5%5Cend%7Barray%7D%5Cright%5D "X = \left[\begin{array}{ccc}1&0\\-1&1\end{array}\right] - \left[\begin{array}{ccc}-2&-8\\2&-4\end{array}\right] \\
X = \left[\begin{array}{ccc}1-(-2)&0 -(-8)\\-1 - 2&1 -(-4)\end{array}\right] \\
X = \left[\begin{array}{ccc}1+2&8\\-3&1+4\end{array}\right] \\
X = \left[\begin{array}{ccc}3&8\\-3&5\end{array}\right]")
B) Achar os valores de a, b, c e d
C) A = aij // aij = 2i - 3j // X + 2A = B
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