Dadas as matrizes ![A \ = \ \left[\begin{array}{ccc}2&-3\\1&4\\\end{array}\right]](https://tex.z-dn.net/?f=A+%5C+%3D+%5C+++%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%26amp%3B-3%5C%5C1%26amp%3B4%5C%5C%5Cend%7Barray%7D%5Cright%5D++ "A \ = \ \left[\begin{array}{ccc}2&-3\\1&4\\\end{array}\right]")
e ![B \ = \ \left[\begin{array}{ccc}1&2\\-1&5\\\end{array}\right] ,](https://tex.z-dn.net/?f=B+%5C+%3D+%5C+++%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%26amp%3B2%5C%5C-1%26amp%3B5%5C%5C%5Cend%7Barray%7D%5Cright%5D+%2C "B \ = \ \left[\begin{array}{ccc}1&2\\-1&5\\\end{array}\right] ,")
determine as matrizes A · B e B · A:
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Achando AB:
![A\cdot B=\left[\begin{array}{cc}2&-3\\1&4\end{array}\right]\cdot\left[\begin{array}{cc}1&2\\-1&5\end{array}\right]\\\\\\A\cdot B=\left[\begin{array}{cc}(2\cdot1+[-3]\cdot[-1])&(2\cdot2+[-3]\cdot5)\\(1\cdot1+4\cdot[-1])&(1\cdot2+4\cdot5)\end{array}\right]\\\\\\A\cdot B=\left[\begin{array}{cc}(2+3)&(4-15)\\(1-4)&(2+20)\end{array}\right]\\\\\\\boxed{\boxed{A\cdot B=\left[\begin{array}{cc}5&-11\\-3&~~22\end{array}\right]}}](https://tex.z-dn.net/?f=A%5Ccdot+B%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D2%26amp%3B-3%5C%5C1%26amp%3B4%5Cend%7Barray%7D%5Cright%5D%5Ccdot%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%26amp%3B2%5C%5C-1%26amp%3B5%5Cend%7Barray%7D%5Cright%5D%5C%5C%5C%5C%5C%5CA%5Ccdot+B%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%282%5Ccdot1%2B%5B-3%5D%5Ccdot%5B-1%5D%29%26amp%3B%282%5Ccdot2%2B%5B-3%5D%5Ccdot5%29%5C%5C%281%5Ccdot1%2B4%5Ccdot%5B-1%5D%29%26amp%3B%281%5Ccdot2%2B4%5Ccdot5%29%5Cend%7Barray%7D%5Cright%5D%5C%5C%5C%5C%5C%5CA%5Ccdot+B%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%282%2B3%29%26amp%3B%284-15%29%5C%5C%281-4%29%26amp%3B%282%2B20%29%5Cend%7Barray%7D%5Cright%5D%5C%5C%5C%5C%5C%5C%5Cboxed%7B%5Cboxed%7BA%5Ccdot+B%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D5%26amp%3B-11%5C%5C-3%26amp%3B%7E%7E22%5Cend%7Barray%7D%5Cright%5D%7D%7D "A\cdot B=\left[\begin{array}{cc}2&-3\\1&4\end{array}\right]\cdot\left[\begin{array}{cc}1&2\\-1&5\end{array}\right]\\\\\\A\cdot B=\left[\begin{array}{cc}(2\cdot1+[-3]\cdot[-1])&(2\cdot2+[-3]\cdot5)\\(1\cdot1+4\cdot[-1])&(1\cdot2+4\cdot5)\end{array}\right]\\\\\\A\cdot B=\left[\begin{array}{cc}(2+3)&(4-15)\\(1-4)&(2+20)\end{array}\right]\\\\\\\boxed{\boxed{A\cdot B=\left[\begin{array}{cc}5&-11\\-3&~~22\end{array}\right]}}")
Achando BA:
![B\cdot A=\left[\begin{array}{cc}1&2\\-1&5\end{array}\right]\cdot\left[\begin{array}{cc}2&-3\\1&4\end{array}\right]\\\\\\B\cdot A=\left[\begin{array}{cc}(1\cdot2+2\cdot1)&(1\cdot[-3]+2\cdot4)\\([-1]\cdot2+5\cdot1)&([-1]\cdot[-3]+5\cdot4)\end{array}\right]\\\\\\B\cdot A=\left[\begin{array}{cc}(2+2)&(-3+8)\\(-2+5)&(3+20)\end{array}\right]\\\\\\\boxed{\boxed{B\cdot A=\left[\begin{array}{cc}4&5\\3&23\end{array}\right]}}](https://tex.z-dn.net/?f=B%5Ccdot+A%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%26amp%3B2%5C%5C-1%26amp%3B5%5Cend%7Barray%7D%5Cright%5D%5Ccdot%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D2%26amp%3B-3%5C%5C1%26amp%3B4%5Cend%7Barray%7D%5Cright%5D%5C%5C%5C%5C%5C%5CB%5Ccdot+A%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%281%5Ccdot2%2B2%5Ccdot1%29%26amp%3B%281%5Ccdot%5B-3%5D%2B2%5Ccdot4%29%5C%5C%28%5B-1%5D%5Ccdot2%2B5%5Ccdot1%29%26amp%3B%28%5B-1%5D%5Ccdot%5B-3%5D%2B5%5Ccdot4%29%5Cend%7Barray%7D%5Cright%5D%5C%5C%5C%5C%5C%5CB%5Ccdot+A%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%282%2B2%29%26amp%3B%28-3%2B8%29%5C%5C%28-2%2B5%29%26amp%3B%283%2B20%29%5Cend%7Barray%7D%5Cright%5D%5C%5C%5C%5C%5C%5C%5Cboxed%7B%5Cboxed%7BB%5Ccdot+A%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D4%26amp%3B5%5C%5C3%26amp%3B23%5Cend%7Barray%7D%5Cright%5D%7D%7D "B\cdot A=\left[\begin{array}{cc}1&2\\-1&5\end{array}\right]\cdot\left[\begin{array}{cc}2&-3\\1&4\end{array}\right]\\\\\\B\cdot A=\left[\begin{array}{cc}(1\cdot2+2\cdot1)&(1\cdot[-3]+2\cdot4)\\([-1]\cdot2+5\cdot1)&([-1]\cdot[-3]+5\cdot4)\end{array}\right]\\\\\\B\cdot A=\left[\begin{array}{cc}(2+2)&(-3+8)\\(-2+5)&(3+20)\end{array}\right]\\\\\\\boxed{\boxed{B\cdot A=\left[\begin{array}{cc}4&5\\3&23\end{array}\right]}}")
Achando BA:
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