Evaluate

$open vertical bar table row cell 1 space end cell cell space straight x end cell straight y row 1 cell space space straight x plus straight y end cell straight y row 1 straight x cell space straight x plus straight y end cell end table close vertical bar$

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Solution

Let space space space space increment space equals space open vertical bar table row cell 1 space end cell cell space straight x end cell straight y row 1 cell space space straight x plus straight y end cell straight y row 1 straight x cell space straight x plus straight y end cell end table close vertical bar space equals space open square brackets table row 1 straight x straight y row 0 cell space space straight y space space end cell 0 row 0 0 straight x end table close square brackets space comma space by space straight R subscript 2 minus straight R subscript 1 minus straight R subscript 3 minus straight R subscript 1 space space space space space space space space space space space space space space equals space space open vertical bar table row straight y cell space space 0 end cell row 0 cell space space 0 end cell end table close vertical bar space equals xy

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