Question

$If space straight f left parenthesis straight x right parenthesis space equals space straight x squared minus 5 straight x plus 7 space. space Find space straight f left parenthesis straight A right parenthesis space where space straight A equals space open square brackets table row 3 1 row cell negative 1 end cell 2 end table close square brackets$

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Solution

Here space straight f left parenthesis straight x right parenthesis space equals straight x squared minus 5 straight x plus 7 therefore space space space space space straight f left parenthesis straight A right parenthesis space equals space straight A squared minus 5 straight A plus space 7 straight I Now space space space space space straight A equals space open square brackets table row 3 cell space space 1 end cell row cell negative 1 end cell cell space space 2 end cell end table close square brackets therefore space space space space space space space space straight A squared space equals space space space open square brackets table row 3 cell space space 1 end cell row cell negative 1 end cell cell space space 2 end cell end table close square brackets space space open square brackets table row 3 cell space space 1 end cell row cell negative 1 end cell cell space space 2 end cell end table close square brackets space equals space open square brackets table row cell 9 minus 1 end cell cell space space 3 plus 2 end cell row cell negative 3 minus 2 end cell cell space space minus 1 plus 4 end cell end table close square brackets equals space open square brackets table row 8 cell space space space 5 end cell row cell negative 5 end cell cell space space 3 end cell end table close square brackets therefore space space space space space space space space straight A squared minus 5 straight A plus 7 space straight I space equals space space open square brackets table row 8 cell space space 5 end cell row cell negative 5 end cell cell space space 3 end cell end table close square brackets minus 5 space space open square brackets table row 3 cell space space space 1 end cell row cell negative 1 end cell cell space space 2 end cell end table close square brackets plus 7 space open square brackets table row 1 cell space space 0 end cell row 0 cell space 1 end cell end table close square brackets space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space space open square brackets table row 8 cell space space 5 end cell row cell negative 5 end cell cell space space 3 end cell end table close square brackets plus space open square brackets table row cell negative 15 end cell cell space space minus 5 end cell row 5 cell space space minus 10 end cell end table close square brackets space plus space open square brackets table row 7 cell space space 0 end cell row 0 cell space 7 end cell end table close square brackets space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space space space space open square brackets table row cell 8 minus 15 plus 7 end cell cell 5 minus 5 plus 0 end cell row cell negative 5 plus 5 plus 0 end cell cell 3 minus 10 plus 7 end cell end table close square brackets space equals space open square brackets table row 0 cell space space 0 end cell row 0 cell space space 0 end cell end table close square brackets space therefore space space space space space space space space space space space space space space space space space space space space space space straight f space left parenthesis straight A right parenthesis space equals straight O space space space space space space space space space space space

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Matrices

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