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Determinants

Question
CBSEENMA12034329

Evaluate the determinants

open vertical bar table row 3 cell negative 1 end cell 2 row 0 cell space space 0 end cell cell negative 1 end cell row 3 cell space 5 end cell 0 end table close vertical bar

Solution
Let space space increment space equals space space open vertical bar table row 3 cell negative 1 end cell 2 row 0 cell space space 0 end cell cell negative 1 end cell row 3 cell space 5 end cell 0 end table close vertical bar
space space space space space space space space space space space space equals space space minus 0 space open vertical bar table row cell negative 1 end cell cell space space minus 2 end cell row cell negative 5 end cell cell space space space 0 end cell end table close vertical bar plus 0 space open vertical bar table row 3 cell space space minus 2 end cell row 3 cell space space 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 3 cell space space minus 2 end cell row 3 cell 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 3 cell space space minus 1 end cell row 3 cell space space minus 5 end cell end table close vertical bar
space space space space space space space space space space space space equals space 0 plus 0 plus left parenthesis negative 15 plus 3 right parenthesis space equals negative 12 space space space

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