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Matrices

Question
CBSEENMA12032971
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If space straight x open parentheses table row 2 row 3 end table close parentheses plus straight y open square brackets table row cell negative 1 end cell row 1 end table close square brackets equals open square brackets table row 10 row 5 end table close square brackets space find the values of x and y.    

Solution
The given matrix equation is
space space space space space space straight x space open parentheses table row 2 row 3 end table close parentheses plus straight y open square brackets table row cell negative 1 end cell row 1 end table close square brackets equals open square brackets table row 10 row 5 end table close square brackets space or space space space space open square brackets table row cell 2 straight x end cell row cell 3 straight x end cell end table close square brackets plus open square brackets table row cell negative straight y end cell row straight y end table close square brackets equals open square brackets table row 10 row 5 end table close square brackets or space open square brackets table row cell 2 straight x minus straight y end cell row cell 3 straight x plus straight y end cell end table close square brackets equals open square brackets table row 10 row 5 end table close square brackets

By definition of equality of matrices, we get,
2x – y= 10    ..,(1)
3x +y = 5    .,.(2)
Adding (1) and (2), we get,
5 x = 15 or x = 3
∴ from (1), 6 – y=-10 ⇒ y = – 4
∴. x = 3, y = – 4.


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