Question

$If space straight A equals open square brackets table row 1 0 row cell negative 1 end cell 7 end table close square brackets$ , find K such that $straight A squared minus 8 straight A space plus space straight K space straight I space equals 0$

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Solution

straight A equals open square brackets table row 1 0 row cell negative 1 end cell 7 end table close square brackets straight A to the power of 2 space equals end exponent open square brackets table row 1 0 row cell negative 1 end cell 7 end table close square brackets open square brackets table row 1 0 row cell negative 1 end cell 7 end table close square brackets equals open square brackets table row cell 1 plus 0 end cell cell 0 plus 0 end cell row cell negative 1 minus 7 end cell cell 0 plus 49 end cell end table close square brackets equals open square brackets table row 1 0 row cell negative 8 end cell 49 end table close square brackets Now space straight A squared minus 8 straight A plus straight K space straight I space equals 0 rightwards double arrow space space open square brackets table row 1 0 row cell negative 8 end cell 49 end table close square brackets plus open square brackets table row 1 0 row cell negative 1 end cell 7 end table close square brackets plus straight k open square brackets table row 1 0 row 0 1 end table close square brackets equals open square brackets table row 0 0 row 0 0 end table close square brackets rightwards double arrow open square brackets table row 1 0 row cell negative 8 end cell 49 end table close square brackets plus open square brackets table row cell negative 8 end cell 0 row 8 cell negative 56 end cell end table close square brackets plus open square brackets table row straight k 0 row 0 straight k end table close square brackets equals open square brackets table row 0 0 row 0 0 end table close square brackets rightwards double arrow open square brackets table row cell 1 minus 8 plus straight k end cell cell 0 plus 0 plus 0 end cell row cell negative 8 plus 8 plus 0 end cell cell 49 minus 56 plus straight k end cell end table close square brackets equals open square brackets table row 0 0 row 0 0 end table close square brackets rightwards double arrow space straight k minus 7 equals 0 space space space space space space rightwards double arrow straight k equals 7.

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Matrices

$If space straight A equals open square brackets table row 1 0 row cell negative 1 end cell 7 end table close square brackets$ , find K such that $straight A squared minus 8 straight A space plus space straight K space straight I space equals 0$

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