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Determinants

Question
CBSEENMA12034328

Find the value of ∆, where
increment space space equals space open vertical bar table row 6 cell space minus 3 end cell cell space space space space 2 end cell row 2 cell space minus 1 end cell cell space space space space 2 end cell row cell negative 10 end cell cell space space space space 5 end cell cell space space space space 2 end cell end table close vertical bar

Solution
Here space increment space space equals space open vertical bar table row 6 cell space minus 3 end cell cell space space space space 2 end cell row 2 cell space minus 1 end cell cell space space space space 2 end cell row cell negative 10 end cell cell space space space space 5 end cell cell space 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 space space equals space space 6 space open vertical bar table row cell negative 1 end cell cell space space 2 end cell row 5 cell space space 2 end cell end table close vertical bar space minus left parenthesis negative 3 right parenthesis space open vertical bar table row 2 cell space space 2 end cell row cell negative 10 end cell cell space space 2 end cell end table close vertical bar space plus 2 space open square brackets table row 2 cell space space minus 1 end cell row cell negative 10 end cell cell space space space space 5 end cell end table close square brackets
space space space space space space space space space space space space space space space space space equals space space 6 space left parenthesis negative 2 plus 10 right parenthesis plus 3 left parenthesis 4 plus 20 right parenthesis plus 2 left parenthesis 10 minus 10 right parenthesis equals space minus 72 plus 72 equals 0

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