Question

$Find space the space value space of space the space determinant open vertical bar table row 5 cell space space space space 1 end cell cell space space space space space space 0 end cell row 2 cell space space space space 3 end cell cell space space minus 1 end cell row cell negative 3 end cell cell space space space space 2 end cell cell space space space space 0 end cell end table close vertical bar space$

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Solution

Let space space space increment space space equals open vertical bar table row 5 cell space space space space 1 end cell cell space space space space space space 0 end cell row 2 cell space space space space 3 end cell cell space space minus 1 end cell row cell negative 3 end cell cell space space space space 2 end cell cell space space space space 0 end cell end table close vertical bar space space space space space space space space space space space space space space space equals space space 5 space open vertical bar table row 3 cell space space minus 1 end cell row 2 cell space space space space space 0 end cell end table close vertical bar space minus 1 space open vertical bar table row 2 cell space space minus 1 end cell row cell negative 3 end cell cell space space space space space 0 end cell end table close vertical bar space plus 0 space open vertical bar table row 2 cell space space 3 end cell row cell negative 3 end cell cell space space space 2 end cell end table close vertical bar space space space space space space space space space space space space space space equals space space 5 space left parenthesis 0 plus 2 right parenthesis minus 1 left parenthesis 0 minus 3 right parenthesis plus 0 left parenthesis 4 plus 9 right parenthesis space space space space space space space space space space space space space space equals space space 10 plus 3 plus 0 space equals 13 space space

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