Find the values of .x and y from the following equation

$2 space open square brackets table row straight X 5 row 7 cell straight Y minus 3 end cell end table close square brackets plus open square brackets table row 3 cell negative 4 end cell row 1 2 end table close square brackets equals open square brackets table row 7 6 row 15 14 end table close square brackets$

Solution

The given matrix equation is

space space space space space space space space space space 2 space open square brackets table row straight X 5 row 7 cell straight Y minus 3 end cell end table close square brackets plus open square brackets table row 3 cell negative 4 end cell row 1 2 end table close square brackets equals open square brackets table row 7 6 row 15 14 end table close square brackets or space space space space space space space 2 space open square brackets table row straight X 5 row 7 cell straight Y minus 3 end cell end table close square brackets equals open square brackets table row 7 6 row 15 14 end table close square brackets minus open square brackets table row 3 cell negative 4 end cell row 1 2 end table close square brackets or space space space space space space space 2 space open square brackets table row straight x 5 row 7 cell straight y minus 3 end cell end table close square brackets equals open square brackets table row cell 7 minus 3 space space space end cell cell 6 plus 4 end cell row cell 15 minus 1 space space space end cell cell 14 minus 2 end cell end table close square brackets therefore space space space space space space space 2 space open square brackets table row cell 2 straight x end cell 10 row 14 cell 2 straight y minus 6 end cell end table close square brackets equals open square brackets table row 4 10 row 14 12 end table close square brackets

By definition of equality of matrices, we have
2.x = 4, 2 y –6 = 12
∴-x = 2, 2y = 18
∴.x = 2, y = 9.

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