Find the value of x which makes the following product equal to I :

$open square brackets table row 2 0 7 row 0 1 0 row 1 2 1 end table close square brackets space open square brackets table row cell negative x end cell cell negative 14 end cell cell 7 x end cell row 0 1 0 row x cell 4 x end cell cell negative 2 x end cell end table close square brackets$

Solution

We space are space given space that open square brackets table row 2 0 7 row 0 1 0 row 1 2 1 end table close square brackets space open square brackets table row cell negative straight x end cell cell negative 14 end cell cell 7 straight x end cell row 0 1 0 row straight x cell 4 straight x end cell cell negative 2 straight x end cell end table close square brackets therefore space space open square brackets table row cell negative 2 straight x plus 7 straight x end cell cell negative 28 straight x plus 28 straight x end cell cell 14 straight x minus 14 straight x end cell row 0 1 0 row cell negative straight x plus straight x end cell cell negative 14 straight x plus 2 plus 4 straight x end cell cell 7 straight x minus 2 straight x end cell end table close square brackets equals space open square brackets table row 1 0 0 row 0 1 0 row 0 0 1 end table close square brackets or open square brackets table row cell 5 straight x end cell 0 0 row 0 1 0 row 0 cell negative 10 straight x plus 2 end cell cell 5 straight x end cell end table close square brackets equals open square brackets table row 1 0 0 row 0 1 0 row 0 0 1 end table close square brackets therefore space space space space 5 straight x equals 1 comma space minus 10 straight x plus 2 equals 0 therefore space space straight x equals begin inline style 1 fifth end style

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