Diketahui A= [ -1 0 ]
[ 2 -4 ]
carilah A pangkat 2 - 5A
Tolong dijawab yah!
[ 2 -4 ]
carilah A pangkat 2 - 5A
Tolong dijawab yah!
Takamori37
Sehingga,
![$\begin{align}A^2-5A&=\left[\begin{array}{cc}-1&0\\2&-4\end{array}\right]^2-5\left[\begin{array}{cc}-1&0\\2&-4\end{array}\right] \\ &=\left[\begin{array}{cc}-1&0\\2&-4\end{array}\right]\left[\begin{array}{cc}-1&0\\2&-4\end{array}\right]+\left[\begin{array}{cc}5&0\\-10&20\end{array}\right] \\ &=\left[\begin{array}{cc}-1.1+0.2&-1.0+0.(-4)\\2.(-1)+(-4)2&2.0+(-4)(-4)\end{array}\right]+\left[\begin{array}{cc}5&0\\-10&20\end{array}\right]\end{align}](https://tex.z-dn.net/?f=%24%5Cbegin%7Balign%7DA%5E2-5A%26%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-1%260%5C%5C2%26-4%5Cend%7Barray%7D%5Cright%5D%5E2-5%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-1%260%5C%5C2%26-4%5Cend%7Barray%7D%5Cright%5D+%5C%5C+%26%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-1%260%5C%5C2%26-4%5Cend%7Barray%7D%5Cright%5D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-1%260%5C%5C2%26-4%5Cend%7Barray%7D%5Cright%5D%2B%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D5%260%5C%5C-10%2620%5Cend%7Barray%7D%5Cright%5D+%5C%5C+%26%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-1.1%2B0.2%26-1.0%2B0.%28-4%29%5C%5C2.%28-1%29%2B%28-4%292%262.0%2B%28-4%29%28-4%29%5Cend%7Barray%7D%5Cright%5D%2B%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D5%260%5C%5C-10%2620%5Cend%7Barray%7D%5Cright%5D%5Cend%7Balign%7D "$\begin{align}A^2-5A&=\left[\begin{array}{cc}-1&0\\2&-4\end{array}\right]^2-5\left[\begin{array}{cc}-1&0\\2&-4\end{array}\right] \\ &=\left[\begin{array}{cc}-1&0\\2&-4\end{array}\right]\left[\begin{array}{cc}-1&0\\2&-4\end{array}\right]+\left[\begin{array}{cc}5&0\\-10&20\end{array}\right] \\ &=\left[\begin{array}{cc}-1.1+0.2&-1.0+0.(-4)\\2.(-1)+(-4)2&2.0+(-4)(-4)\end{array}\right]+\left[\begin{array}{cc}5&0\\-10&20\end{array}\right]\end{align}")
![$\begin{align}A^2-5A&=\left[\begin{array}{cc}-1&0\\-10&16\end{array}\right]+\left[\begin{array}{cc}5&0\\-10&20\end{array}\right] \\ &=\left[\begin{array}{cc}4&0\\-20&36\end{array}\right]\end{align}](https://tex.z-dn.net/?f=%24%5Cbegin%7Balign%7DA%5E2-5A%26%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-1%260%5C%5C-10%2616%5Cend%7Barray%7D%5Cright%5D%2B%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D5%260%5C%5C-10%2620%5Cend%7Barray%7D%5Cright%5D+%5C%5C+%26%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D4%260%5C%5C-20%2636%5Cend%7Barray%7D%5Cright%5D%5Cend%7Balign%7D "$\begin{align}A^2-5A&=\left[\begin{array}{cc}-1&0\\-10&16\end{array}\right]+\left[\begin{array}{cc}5&0\\-10&20\end{array}\right] \\ &=\left[\begin{array}{cc}4&0\\-20&36\end{array}\right]\end{align}")
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