Question

$If space straight A equals open square brackets table row 1 0 row cell negative 1 end cell 7 end table close square brackets space and space straight I equals open square brackets table row 1 0 row 0 1 end table close square brackets comma$ 2 = 8 A + k I.

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Solution

Here space straight A equals space open square brackets table row 1 0 row cell negative 1 end cell 7 end table close square brackets space and space straight I equals open square brackets table row 1 0 row 0 1 end table close square brackets Now space space straight A squared minus 8 space straight A plus straight K space straight I rightwards double arrow space space open square brackets table row 1 0 row cell negative 1 end cell 7 end table close square brackets space open square brackets table row 1 0 row cell negative 1 end cell 7 end table close square brackets space equals 8 space open square brackets table row 1 0 row cell negative 1 end cell 7 end table close square brackets plus straight k space open square brackets table row 1 0 row 0 cell 1 space end cell end table close square brackets rightwards double arrow 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 space open square brackets table row 8 0 row cell negative 8 end cell 56 end table close square brackets space plus open square brackets table row straight k 0 row 0 straight k 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 equals open square brackets table row cell straight k plus 8 end cell 0 row cell negative 8 end cell cell straight k plus 56 end cell end table close square brackets rightwards double arrow straight k plus 8 equals 1 comma space space straight k plus 56 equals 49 space space space space space space space space rightwards double arrow space straight k equals 7

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Matrices

$If space straight A equals open square brackets table row 1 0 row cell negative 1 end cell 7 end table close square brackets space and space straight I equals open square brackets table row 1 0 row 0 1 end table close square brackets comma$ 2 = 8 A + k I.

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