Question

Evaluate the determinant

$increment space space equals space space open vertical bar table row 1 cell space space 2 end cell cell space space space 4 end cell row cell negative 1 end cell cell space space 3 end cell cell space space 0 end cell row 4 cell space 1 end cell cell space space 0 end cell end table close vertical bar$

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Solution

increment space space equals space space open vertical bar table row 1 cell space space 2 end cell cell space space space 4 end cell row cell negative 1 end cell cell space space 3 end cell cell space space 0 end cell row 4 cell space 1 end cell cell space space 0 end cell end table close vertical bar space equals 4 space space open square brackets table row cell negative 1 end cell cell space space space 3 end cell row 4 cell space space 1 end cell end table close square brackets space minus 0 space open vertical bar table row 1 cell space space space 2 end cell row 4 cell space space space 1 end cell end table close vertical bar space plus 0 space open vertical bar table row 1 cell space space 2 end cell row cell negative 1 end cell cell space space 3 end cell end table close vertical bar space space space space space space equals space 4 left parenthesis negative 1 minus 12 right parenthesis minus 0 plus 0 equals 4 left parenthesis negative 13 right parenthesis equals negative 52

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