Using cofactors of elements of second row, evaluate:
$increment space equals space open vertical bar table row 5 cell space space 3 end cell cell space space 8 end cell row 2 cell space space 0 end cell cell space space 1 end cell row 1 cell space 2 end cell cell space space 3 end cell end table close vertical bar$

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Solution

increment space equals space open vertical bar table row 5 cell space space space space 3 end cell cell space space 8 end cell row 2 cell space space space 0 end cell cell space space space 1 space space end cell row 1 cell space space 2 end cell cell space space 3 end cell end table close vertical bar space straight A subscript 21 space equals space left parenthesis negative 1 right parenthesis to the power of 2 plus 1 end exponent space open vertical bar table row 3 cell space space space 8 end cell row 2 cell space space space 3 end cell end table close vertical bar space equals space minus left parenthesis 9 minus 16 right parenthesis space equals space 7 straight A subscript 22 space equals space left parenthesis negative 1 right parenthesis to the power of 2 plus 2 end exponent space open vertical bar table row 5 cell space space space 8 end cell row 1 cell space space space 3 end cell end table close vertical bar space equals space 1 left parenthesis 15 minus 8 right parenthesis space equals space 7 straight A subscript 23 space equals space left parenthesis negative 1 right parenthesis to the power of 2 plus 3 end exponent space open vertical bar table row 5 cell space space space space 3 end cell row 1 cell space space space space 2 end cell end table close vertical bar space equals space minus left parenthesis 10 minus 3 right parenthesis space equals space minus 7

Now

increment space equals space straight a subscript 21 straight A subscript 21 plus straight a subscript 22 straight A subscript 22 plus straight a subscript 23 straight A subscript 23

equals space left parenthesis 2 right parenthesis thin space left parenthesis 7 right parenthesis space plus space left parenthesis 0 right parenthesis thin space left parenthesis 7 right parenthesis space plus space left parenthesis 1 right parenthesis thin space left parenthesis negative 7 right parenthesis space equals space 14 plus 0 minus 7 space equals space 7

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