Question

$Evaluate space the space determinants open vertical bar table row 2 cell space space space minus 1 end cell cell space space minus 2 end cell row 0 cell space space space space space space 2 end cell cell space space space space 1 end cell row 3 cell space space minus 5 end cell cell space space space space 0 end cell end table close vertical bar$

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Solution

Let space increment space equals space open vertical bar table row 2 cell space space space minus 1 end cell cell space space minus 2 end cell row 0 cell space space space space space space space 2 end cell cell space space minus 1 end cell row 3 cell space space minus 5 end cell cell space space space space 0 end cell end table close vertical bar space equals 2 space open vertical bar table row 2 cell space minus 1 end cell row cell negative 5 end cell cell space space space space 0 end cell end table close vertical bar space minus left parenthesis negative 1 right parenthesis space open vertical bar table row 0 cell space space minus 1 end cell row 3 cell space space space space space space 0 end cell end table close vertical bar plus left parenthesis negative 2 right parenthesis space open vertical bar table row 0 cell space space space space 2 end cell row 3 cell space minus 5 end cell end table close vertical bar space space space space space space space space space space space equals space space 2 left parenthesis 0 minus 5 right parenthesis plus 1 left parenthesis 0 plus 3 right parenthesis minus 2 left parenthesis 0 minus 6 right parenthesis space space space space space space space space space space space equals space space 2 left parenthesis negative 5 right parenthesis plus 1 left parenthesis 3 right parenthesis minus 2 left parenthesis negative 6 right parenthesis equals negative 10 plus 3 plus 12 equals 5

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