Question

if A= $\left[\begin{array}{ccc}4&5&-3\\2&1&0\\6&7&2\end{array}\right]$ b=$\left[\begin{array}{ccc}3&2&1\\7&8&4\\5&6&-2\end{array}\right]$ find matrix 'X' such that 2a+3b-5x=0    want proper steps urgent !!!!!!!!

Answer 1

$2A=2\times\left[\begin{array}{ccc}4&5&-3\\2&1&0\\6&7&2\end{array}\right]= \left[\begin{array}{ccc}8&10&-6\\4&2&0\\12&14&4\end{array}\right] \\3B=3\times \left[\begin{array}{ccc}3&2&1\\7&8&4\\5&6&-2\end{array}\right] = \left[\begin{array}{ccc}9&6&3\\21&24&12\\15&18&-6\end{array}\right]$

$2A+3B=\left[\begin{array}{ccc}8&10&-6\\4&2&0\\12&14&4\end{array}\right]+\left[\begin{array}{ccc}9&6&3\\21&24&12\\15&18&-6\end{array}\right]= \left[\begin{array}{ccc}17&16&-3\\25&26&12\\27&32&-2\end{array}\right] \\X= \left[\begin{array}{ccc}x_1&x_2&x_3\\x_4&x_5&x_6\\x_7&x_8&x_9\end{array}\right]\Rightarrow5X=\left[\begin{array}{ccc}5x_1&5x_2&5x_3\\5x_4&5x_5&5x_6\\5x_7&5x_8&5x_9\end{array}\right]\\\\2A+3B-5X=0\iff2A+3B=5X\\\Updownarrow$
$\left[\begin{array}{ccc}17&16&-3\\25&26&12\\27&32&-2\end{array}\right]=\left[\begin{array}{ccc}5x_1&5x_2&5x_3\\5x_4&5x_5&5x_6\\5x_7&5x_8&5x_9\end{array}\right]\\\Updownarrow\\X= \left[\begin{array}{ccc}\frac{17}{5}&\frac{16}{5}&-\frac{3}{5}\\5&\frac{26}{5}&\frac{12}{5}\\\frac{27}{5}&\frac{32}{5}&-\frac{2}{5}\end{array}\right]= \left[\begin{array}{ccc}3.4&3.2&-0.6\\5&5.2&2.4\\5.4&6.4&-0.4\end{array}\right]$