Question

Solve the matrix equation

$space space space space space space open square brackets table row cell straight x squared end cell row cell straight y squared end cell end table close square brackets minus 3 space open square brackets table row x row cell 2 space y end cell end table close square brackets equals open square brackets table row cell negative 2 end cell row 9 end table close square brackets space$

Solution

space space space space space open square brackets table row cell straight x squared end cell row cell straight y squared end cell end table close square brackets minus 3 space open square brackets table row straight x row cell 2 space straight y end cell end table close square brackets equals open square brackets table row cell negative 2 end cell row 9 end table close square brackets or space space space open square brackets table row cell straight x squared end cell row cell straight y squared end cell end table close square brackets plus open square brackets table row cell negative 3 space straight x end cell row cell negative 6 straight y end cell end table close square brackets equals open square brackets table row cell negative 2 end cell row 9 end table close square brackets therefore space space space open square brackets table row cell straight x squared minus 3 straight x end cell row cell straight y squared minus 6 straight y end cell end table close square brackets equals open square brackets table row cell negative 2 end cell row 9 end table close square brackets

⇒ x² – 3 .x = – 2 or ,x²–3.x + 2 = 0 ...(I)
and y²-6y=9 or y²-6y-9 = 0 ...(2)
From(l), (.x –1) (.x – 2) = 0 ⇒ x = 1,2

From space left parenthesis 2 right parenthesis space space straight y equals fraction numerator 6 plus-or-minus square root of 36 plus 36 end root over denominator 2 end fraction equals fraction numerator 6 plus-or-minus square root of 72 over denominator 2 end fraction equals fraction numerator 6 plus-or-minus 6 square root of 2 over denominator 2 end fraction equals 3 plus-or-minus 3 square root of 2

∴ we have
x=1, 2 ; y =

3 plus-or-minus 3 square root of 2

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