Question

Please help me and explain the Matrices problem as follows:
Find X and Y if 2X+3Y = [2 3] and 3X + 2Y = [2 -2]
[4 0] [-1 5]

Answer 1

$2 X + 3 Y = \left[\begin{array}{ccc}2&3\\4&0\end{array}\right] \\\\3 X + 2 Y = \left[\begin{array}{ccc}2&-2\\-1&5\end{array}\right] \\\\2*(2 X + 3 Y) = \left[\begin{array}{ccc}2*2&2*3\\2*4&2*0\end{array}\right]\\\\-3*(3 X + 2 Y) = \left[\begin{array}{ccc}-3*2&-3*-2\\-3*-1&-3*5\end{array}\right]\\\\Adding\ the\ above\ two\ matrices\\\\4X+6Y-9X-6Y=\left[\begin{array}{ccc}2*2-3*2&2*3-3*-2\\2*4-3*-1&0-3*5\end{array}\right]\\\\-5X=\left[\begin{array}{ccc}-2&12\\11&-15\end{array}\right]$

$X= \left[\begin{array}{ccc}2/5&-12/5\\11/5&3\end{array}\right]\\\\using\ 1st\ equation\\\\3*\ Y=\left[\begin{array}{ccc}2&3\\4&0\end{array}\right]-2*\left[\begin{array}{ccc}2/5&-12/5\\11/5&3\end{array}\right]=\left[\begin{array}{ccc}2-4/5&3+24/5\\4-22/5&0-2*3\end{array}\right]\\\\Y=\left[\begin{array}{ccc}2/5&13/5\\-2/15&-2\end{array}\right]$

..We solve the matrix equations just like simultaneous in variables.