Find matrices X and Y, if

$2 straight X minus straight Y equals open square brackets table row 6 cell negative 6 end cell 0 row cell negative 4 end cell 2 1 end table close square brackets space and space straight x plus 2 straight y equals open square brackets table row 3 2 5 row cell negative 2 end cell 1 cell negative 7 end cell end table close square brackets space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space$

Solution

The given equations are

space space space space space space space space space space space space 2 straight X minus straight Y equals open square brackets table row 6 cell negative 6 end cell 0 row cell negative 4 end cell 2 1 end table close square brackets space space space space space space space space space space space space... left parenthesis 1 right parenthesis space and space space space space space space space straight x plus 2 straight y equals open square brackets table row 3 2 5 row cell negative 2 end cell 1 cell negative 7 end cell end table close square brackets space space space space space space space space space space space space... left parenthesis 2 right parenthesis From space left parenthesis 1 right parenthesis space straight Y space equals space 2 straight C minus open square brackets table row 6 cell negative 6 end cell 0 row cell negative 4 end cell 2 1 end table close square brackets space space space space space space space space space... left parenthesis 3 right parenthesis space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space

from (2) and (3), we get,
$straight X plus 4 straight X minus 2 open square brackets table row 6 cell negative 6 end cell 0 row cell negative 4 end cell 2 1 end table close square brackets equals open square brackets table row 3 2 5 row cell negative 2 end cell 1 cell negative 7 end cell end table close square brackets therefore space space space space space space 5 straight X space equals open square brackets table row 3 2 5 row cell negative 2 end cell 1 cell negative 7 end cell end table close square brackets space plus 2 space open square brackets table row 6 cell negative 6 end cell 0 row cell negative 4 end cell 2 1 end table close square brackets space space space space space space space space space space space space space equals open square brackets table row 3 2 5 row cell negative 2 end cell 1 cell negative 7 end cell end table close square brackets plus 2 space open square brackets table row 12 cell negative 12 end cell 0 row cell negative 8 end cell 4 2 end table close square brackets therefore space space space space space space 5 straight X space equals space open square brackets table row cell 3 plus 12 end cell cell 2 minus 12 end cell cell 5 plus 0 end cell row cell negative 2 minus 8 end cell cell 1 plus 4 end cell cell negative 7 plus 2 end cell end table close square brackets rightwards double arrow space space space space space 5 straight X equals open square brackets table row 15 cell negative 10 end cell 5 row cell negative 10 end cell 5 cell negative 5 end cell end table close square brackets therefore space space space space space space straight X equals 1 over 15 open square brackets table row 15 cell negative 10 end cell 5 row cell negative 10 end cell 5 cell negative 5 end cell end table close square brackets space space space space rightwards double arrow space space straight X equals open square brackets table row 3 cell negative 2 end cell 1 row cell negative 2 end cell 1 cell negative 1 end cell end table close square brackets$

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Matrices

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