A = [7 4]
[-9 -5]
det(A^10) adalah? tolong pembahasannya
[-9 -5]
det(A^10) adalah? tolong pembahasannya
izharulhaq78
![\displaystyle A=\left[\begin{array}{ccc}7&4\\-9&-5\end{array}\right]\\\\|A|=7\times(-5)-(-9)\times4\\|A|=-35-(-36)\\|A|=-35+36\\|A|=1](https://tex.z-dn.net/?f=%5Cdisplaystyle+A%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D7%264%5C%5C-9%26-5%5Cend%7Barray%7D%5Cright%5D%5C%5C%5C%5C%7CA%7C%3D7%5Ctimes%28-5%29-%28-9%29%5Ctimes4%5C%5C%7CA%7C%3D-35-%28-36%29%5C%5C%7CA%7C%3D-35%2B36%5C%5C%7CA%7C%3D1 "\displaystyle A=\left[\begin{array}{ccc}7&4\\-9&-5\end{array}\right]\\\\|A|=7\times(-5)-(-9)\times4\\|A|=-35-(-36)\\|A|=-35+36\\|A|=1")
![\displaystyle A^2=A\times A\\A^2=\left[\begin{array}{ccc}7&4\\-9&-5\end{array}\right]\left[\begin{array}{ccc}7&4\\-9&-5\end{array}\right]\\A^2=\left[\begin{array}{ccc}7\times7+4\times(-9)&7\times4+4\times(-5)\\-9\times7+(-5)\times(-9)&-9\times4+(-5)\times(-5)\end{array}\right]\\A^2=\left[\begin{array}{ccc}49-36&28-20\\-36+45&-36+25\end{array}\right]\\A^2=\left[\begin{array}{ccc}13&8\\-18&-11\end{array}\right]](https://tex.z-dn.net/?f=%5Cdisplaystyle+A%5E2%3DA%5Ctimes+A%5C%5CA%5E2%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D7%264%5C%5C-9%26-5%5Cend%7Barray%7D%5Cright%5D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D7%264%5C%5C-9%26-5%5Cend%7Barray%7D%5Cright%5D%5C%5CA%5E2%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D7%5Ctimes7%2B4%5Ctimes%28-9%29%267%5Ctimes4%2B4%5Ctimes%28-5%29%5C%5C-9%5Ctimes7%2B%28-5%29%5Ctimes%28-9%29%26-9%5Ctimes4%2B%28-5%29%5Ctimes%28-5%29%5Cend%7Barray%7D%5Cright%5D%5C%5CA%5E2%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D49-36%2628-20%5C%5C-36%2B45%26-36%2B25%5Cend%7Barray%7D%5Cright%5D%5C%5CA%5E2%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D13%268%5C%5C-18%26-11%5Cend%7Barray%7D%5Cright%5D "\displaystyle A^2=A\times A\\A^2=\left[\begin{array}{ccc}7&4\\-9&-5\end{array}\right]\left[\begin{array}{ccc}7&4\\-9&-5\end{array}\right]\\A^2=\left[\begin{array}{ccc}7\times7+4\times(-9)&7\times4+4\times(-5)\\-9\times7+(-5)\times(-9)&-9\times4+(-5)\times(-5)\end{array}\right]\\A^2=\left[\begin{array}{ccc}49-36&28-20\\-36+45&-36+25\end{array}\right]\\A^2=\left[\begin{array}{ccc}13&8\\-18&-11\end{array}\right]")
![\displaystyle A^2=\left[\begin{array}{ccc}13&8\\-18&-11\end{array}\right]\\\\|A^2|=13\times(-11)-(-18)\times8\\|A^2|=-143-(-144)\\|A^2|=-143+144\\|A^2|=1](https://tex.z-dn.net/?f=%5Cdisplaystyle+A%5E2%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D13%268%5C%5C-18%26-11%5Cend%7Barray%7D%5Cright%5D%5C%5C%5C%5C%7CA%5E2%7C%3D13%5Ctimes%28-11%29-%28-18%29%5Ctimes8%5C%5C%7CA%5E2%7C%3D-143-%28-144%29%5C%5C%7CA%5E2%7C%3D-143%2B144%5C%5C%7CA%5E2%7C%3D1 "\displaystyle A^2=\left[\begin{array}{ccc}13&8\\-18&-11\end{array}\right]\\\\|A^2|=13\times(-11)-(-18)\times8\\|A^2|=-143-(-144)\\|A^2|=-143+144\\|A^2|=1")
![\displaystyle A^3=A^2\times A\\A^3=\left[\begin{array}{ccc}13&8\\-18&-11\end{array}\right]\left[\begin{array}{ccc}7&4\\-9&-5\end{array}\right]\\A^3=\left[\begin{array}{ccc}13\times7+8\times(-9)&13\times4+8\times(-5)\\-18\times7+(-11)\times(-9)&-18\times4+(-11)\times(-5)\end{array}\right]\\A^3=\left[\begin{array}{ccc}91-72&52-40\\-126+99&-72+55\end{array}\right]\\A^3=\left[\begin{array}{ccc}19&12\\-27&-17\end{array}\right]](https://tex.z-dn.net/?f=%5Cdisplaystyle+A%5E3%3DA%5E2%5Ctimes+A%5C%5CA%5E3%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D13%268%5C%5C-18%26-11%5Cend%7Barray%7D%5Cright%5D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D7%264%5C%5C-9%26-5%5Cend%7Barray%7D%5Cright%5D%5C%5CA%5E3%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D13%5Ctimes7%2B8%5Ctimes%28-9%29%2613%5Ctimes4%2B8%5Ctimes%28-5%29%5C%5C-18%5Ctimes7%2B%28-11%29%5Ctimes%28-9%29%26-18%5Ctimes4%2B%28-11%29%5Ctimes%28-5%29%5Cend%7Barray%7D%5Cright%5D%5C%5CA%5E3%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D91-72%2652-40%5C%5C-126%2B99%26-72%2B55%5Cend%7Barray%7D%5Cright%5D%5C%5CA%5E3%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D19%2612%5C%5C-27%26-17%5Cend%7Barray%7D%5Cright%5D "\displaystyle A^3=A^2\times A\\A^3=\left[\begin{array}{ccc}13&8\\-18&-11\end{array}\right]\left[\begin{array}{ccc}7&4\\-9&-5\end{array}\right]\\A^3=\left[\begin{array}{ccc}13\times7+8\times(-9)&13\times4+8\times(-5)\\-18\times7+(-11)\times(-9)&-18\times4+(-11)\times(-5)\end{array}\right]\\A^3=\left[\begin{array}{ccc}91-72&52-40\\-126+99&-72+55\end{array}\right]\\A^3=\left[\begin{array}{ccc}19&12\\-27&-17\end{array}\right]")
![\displaystyle A^3=\left[\begin{array}{ccc}19&12\\-27&-17\end{array}\right]\\\\|A^3|=19\times(-17)-(-27)\times12\\|A^3|=-323-(-324)\\|A^3|=-323+324\\|A^3|=1](https://tex.z-dn.net/?f=%5Cdisplaystyle+A%5E3%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D19%2612%5C%5C-27%26-17%5Cend%7Barray%7D%5Cright%5D%5C%5C%5C%5C%7CA%5E3%7C%3D19%5Ctimes%28-17%29-%28-27%29%5Ctimes12%5C%5C%7CA%5E3%7C%3D-323-%28-324%29%5C%5C%7CA%5E3%7C%3D-323%2B324%5C%5C%7CA%5E3%7C%3D1 "\displaystyle A^3=\left[\begin{array}{ccc}19&12\\-27&-17\end{array}\right]\\\\|A^3|=19\times(-17)-(-27)\times12\\|A^3|=-323-(-324)\\|A^3|=-323+324\\|A^3|=1")
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