Question

$Find space the space value space of space the space determinant open vertical bar table row 212 cell space space space space 117 space space end cell cell space space 345 end cell row 19 cell space space 9 end cell cell space space 34 end cell row 7 cell space space 3 end cell cell space space 5 end cell end table close vertical bar$

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Solution

Let space space increment space equals space open vertical bar table row 212 cell space space space space 117 space space end cell cell space space 345 end cell row 19 cell space space 9 end cell cell space space 34 end cell row 7 cell space space 3 end cell cell space space 5 end cell end table close vertical bar space space space space space space space space space space space equals 212 space space open vertical bar table row 9 cell space space space 34 end cell row 3 cell space space space 5 end cell end table close vertical bar space minus 117 space open vertical bar table row 19 cell space space 34 end cell row 7 cell space space space 5 end cell end table close vertical bar plus 345 space open vertical bar table row cell 19 space end cell cell space 9 end cell row 7 cell space space 3 end cell end table close vertical bar space space space space space space space space space space space equals 212 space left parenthesis 45 minus 102 right parenthesis minus 117 left parenthesis 95 minus 238 right parenthesis plus 345 left parenthesis 57 minus 63 right parenthesis space space space space space space space space space space space space equals negative 12084 plus 16731 minus 2070 equals 2577

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