Question

If A, $open square brackets table row 2 cell negative 3 end cell row cell negative 4 end cell 1 end table close square brackets$ then adj (3A2 + 12A) is equal to

$open square brackets table row 72 cell negative 63 end cell row cell negative 84 end cell 51 end table close square brackets$
$open square brackets table row 72 cell negative 84 end cell row cell negative 63 end cell 51 end table close square brackets$
$open square brackets table row 51 63 row 84 72 end table close square brackets$
$open square brackets table row 51 84 row 63 72 end table close square brackets$

Solution

open square brackets table row 51 63 row 84 72 end table close square brackets

Given space straight A space equals space open square brackets table row 2 cell negative 3 end cell row cell negative 4 end cell 1 end table close square brackets 3 straight A squared space equals space open square brackets table row 16 cell negative 9 end cell row cell negative 12 end cell 13 end table close square brackets 12 space straight A space equals space open square brackets table row 24 cell negative 36 end cell row cell negative 48 end cell 12 end table close square brackets therefore space 3 straight A squared space plus space 12 space straight A space equals space open square brackets table row 72 cell negative 63 end cell row cell negative 84 end cell 51 end table close square brackets adj space left parenthesis 3 straight A squared space plus space 12 space straight A right parenthesis space equals space open square brackets table row 51 63 row 84 72 end table close square brackets

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