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Determinants

Question
CBSEENMA12034331

open vertical bar table row 0 cell space space space space 1 end cell cell space space space space space 2 end cell row cell negative 1 end cell cell space space space space 0 end cell cell space space minus 3 end cell row cell negative 2 end cell cell space space space space 3 end cell cell space space space 0 end cell end table close vertical bar

Solution
Let space space space increment space equals space open vertical bar table row 0 cell space space space space 1 end cell cell space space space space space 2 end cell row cell negative 1 end cell cell space space space space 0 end cell cell space space minus 3 end cell row cell negative 2 end cell cell space space space space 3 end cell cell space space space 0 end cell end table close vertical bar
space space space space space space space space space space space space equals space 0 space open vertical bar table row 0 cell space space space minus 3 end cell row 3 cell space space 0 end cell end table close vertical bar space minus 1 space open vertical bar table row cell negative 1 end cell cell space space minus 3 end cell row cell negative 2 end cell cell space space space space space 0 end cell end table close vertical bar space plus 2 space open square brackets table row cell negative 1 end cell cell space space 0 end cell row cell negative 2 end cell cell space space 3 end cell end table close square brackets
space space space space space space space space space space space space equals space 0 minus 1 left parenthesis 0 minus 6 right parenthesis plus 2 left parenthesis 3 minus 0 right parenthesis equals 0 plus 6 minus 6 equals 0

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