Question

4th question please send me the answers fast.... please
tomorrow I have exams​

Answer 1

Step-by-step explanation:

$A=\left[\begin{array}{ccc}2&3&4\\0&-2&1\\0&-2&2\end{array}\right] \\\\\\B=\left[\begin{array}{ccc}2&0&-3\\0&0&-1\\3&4&5\end{array}\right] \\\\\\C=\left[\begin{array}{ccc}5&6&7\\-1&2&3\\4&-5&4\end{array}\right] \\\\\\A(BC)=(AB)C\\\\LHS\\\\A(BC)\\\\=\left[\begin{array}{ccc}2&3&4\\0&-2&1\\0&-2&2\end{array}\right] \left( \left[\begin{array}{ccc}2&0&-3\\0&0&-1\\3&4&5\end{array}\right] \left[\begin{array}{ccc}5&6&7\\-1&2&3\\4&-5&4\end{array}\right]\right)$

$=\left[\begin{array}{ccc}2&3&4\\0&-2&1\\0&-2&2\end{array}\right] \left[\begin{array}{ccc}10+0-12&12+0+15&14+0-12\\0+0-4&0+0+5&0+0-4\\15-4+20&18+8-25&21+12+20\end{array}\right] \\\\\\=\left[\begin{array}{ccc}2&3&4\\0&-2&1\\0&-2&2\end{array}\right] \left[\begin{array}{ccc}-2&27&-2\\-4&5&-4\\31&1&53\end{array}\right] \\\\\\=\left[\begin{array}{ccc}-4-12+124&54+15+4&-4-12+212\\0+8+31&0-10+1&0+8+53\\0+8+62&0-10+2&0+8+106\end{array}\right]$

$=\left[\begin{array}{ccc}108&73&206\\39&-9&61\\70&-8&114\end{array}\right]$

$RHS\\\\(AB).C\\\\=\left(\left[\begin{array}{ccc}2&3&4\\0&-2&1\\0&-2&2\end{array}\right] \left[\begin{array}{ccc}2&0&-3\\0&0&-1\\3&4&5\end{array}\right] \right)\left[\begin{array}{ccc}5&6&7\\-1&2&3\\4&-5&4\end{array}\right] \\\\\\=\left[\begin{array}{ccc}4+0+12&0+0+16&-6-3+20\\0+0+3&0+0+4&0+2+5\\0+0+6&0+0+8&0+2+10\end{array}\right] \left[\begin{array}{ccc}5&6&7\\-1&2&3\\4&-5&4\end{array}\right]$

$=\left[\begin{array}{ccc}16&16&11\\3&4&7\\6&8&12\end{array}\right]\left[\begin{array}{ccc}5&6&7\\-1&2&3\\4&-5&4\end{array}\right] \\\\\\=\left[\begin{array}{ccc}80-16+44&96+32-55&112+48+44\\15-4+28&18+8-35&21+12+28\\30-8+48&36+16-60&42+24+48\end{array}\right] \\\\\\=\left[\begin{array}{ccc}108&73&206\\39&-9&61\\70&-8&114\end{array}\right]$

Therefore  A(BC)=(AB)C