Find matrices X and Y if X + Y = $open square brackets table row 5 2 row 0 9 end table close square brackets space and space straight X minus straight Y space open square brackets table row 3 6 row 0 cell negative 1 end cell end table close square brackets$

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Solution

We have

straight X plus straight Y equals open square brackets table row 5 2 row 0 9 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 space space space comma comma comma left parenthesis 1 right parenthesis straight X minus straight Y equals open square brackets table row 3 6 row 0 cell negative 1 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... left parenthesis 2 right parenthesis

Adding (1) and (2), we get,

2 space straight X equals open square brackets table row 8 8 row 0 8 end table close square brackets space space space space space space rightwards double arrow space space straight X equals open square brackets table row 4 4 row 0 4 end table close square brackets

Subtracting (2) from (1), we get,

2 space straight Y space equals space open square brackets table row 2 cell negative 4 end cell row 0 10 end table close square brackets space space space space space space rightwards double arrow space space straight Y equals open square brackets table row 1 cell negative 2 end cell row 0 5 end table close square brackets

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