Jika matriks A= (-1 2)
(3 -2)
dan A pangkat 2 = xA + yI maka x+y=..
(3 -2)
dan A pangkat 2 = xA + yI maka x+y=..
kekkaiisshi
![A = \left[\begin{array}{ccc}-1&2\\3&-2\end{array}\right] \\ A^{2} = A.A = \left[\begin{array}{ccc}-1&2\\3&-2\end{array}\right].\left[\begin{array}{ccc}-1&2\\3&-2\end{array}\right] \\ A^{2}=\left[\begin{array}{ccc}7&-6\\-9&10\end{array}\right]](https://tex.z-dn.net/?f=A+%3D+++%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-1%262%5C%5C3%26-2%5Cend%7Barray%7D%5Cright%5D++%5C%5C+A%5E%7B2%7D+%3D+A.A+%3D+%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-1%262%5C%5C3%26-2%5Cend%7Barray%7D%5Cright%5D.%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-1%262%5C%5C3%26-2%5Cend%7Barray%7D%5Cright%5D+%5C%5C+A%5E%7B2%7D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D7%26-6%5C%5C-9%2610%5Cend%7Barray%7D%5Cright%5D "A = \left[\begin{array}{ccc}-1&2\\3&-2\end{array}\right] \\ A^{2} = A.A = \left[\begin{array}{ccc}-1&2\\3&-2\end{array}\right].\left[\begin{array}{ccc}-1&2\\3&-2\end{array}\right] \\ A^{2}=\left[\begin{array}{ccc}7&-6\\-9&10\end{array}\right]")
![A^{2} = x \left[\begin{array}{ccc}-1&2\\3&-2\end{array}\right] +y \left[\begin{array}{ccc}1&0\\0&1\end{array}\right] \\ \\ \left[\begin{array}{ccc}7&-6\\-9&10\end{array}\right] = \left[\begin{array}{ccc}-x&2x\\3x&-2x\end{array}\right] + \left[\begin{array}{ccc}y&0\\0&y\end{array}\right] \\ \left[\begin{array}{ccc}7&-6\\-9&10\end{array}\right] = \left[\begin{array}{ccc}-x+y&2x\\3x&-2x+y\end{array}\right] \\ -6 = 2x \\ -3 = x \\ \\ -x + y = 7 \\ -(-3) + y = 7 \\ y = 7 - 3 \\ y = 4 \\ x + y = -3 + 4 = -1](https://tex.z-dn.net/?f=A%5E%7B2%7D+%3D+x++%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-1%262%5C%5C3%26-2%5Cend%7Barray%7D%5Cright%5D+%2By++%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%260%5C%5C0%261%5Cend%7Barray%7D%5Cright%5D++%5C%5C++%5C%5C+%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D7%26-6%5C%5C-9%2610%5Cend%7Barray%7D%5Cright%5D+%3D+%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-x%262x%5C%5C3x%26-2x%5Cend%7Barray%7D%5Cright%5D+%2B+%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dy%260%5C%5C0%26y%5Cend%7Barray%7D%5Cright%5D+%5C%5C+%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D7%26-6%5C%5C-9%2610%5Cend%7Barray%7D%5Cright%5D+%3D+%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-x%2By%262x%5C%5C3x%26-2x%2By%5Cend%7Barray%7D%5Cright%5D+%5C%5C+-6+%3D+2x+%5C%5C+-3+%3D+x+%5C%5C++%5C%5C+-x+%2B+y+%3D+7+%5C%5C+-%28-3%29+%2B+y+%3D+7+%5C%5C+y+%3D+7+-+3+%5C%5C+y+%3D+4+%5C%5C+x+%2B+y+%3D+-3+%2B+4+%3D+-1 "A^{2} = x \left[\begin{array}{ccc}-1&2\\3&-2\end{array}\right] +y \left[\begin{array}{ccc}1&0\\0&1\end{array}\right] \\ \\ \left[\begin{array}{ccc}7&-6\\-9&10\end{array}\right] = \left[\begin{array}{ccc}-x&2x\\3x&-2x\end{array}\right] + \left[\begin{array}{ccc}y&0\\0&y\end{array}\right] \\ \left[\begin{array}{ccc}7&-6\\-9&10\end{array}\right] = \left[\begin{array}{ccc}-x+y&2x\\3x&-2x+y\end{array}\right] \\ -6 = 2x \\ -3 = x \\ \\ -x + y = 7 \\ -(-3) + y = 7 \\ y = 7 - 3 \\ y = 4 \\ x + y = -3 + 4 = -1")
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