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Determinants

Question
CBSEENMA12034381
Wired Faculty App

show space that space open vertical bar table row straight a cell space space space space space space space space space space space space straight a plus straight b end cell cell space straight a plus straight b plus straight c end cell row cell 2 straight a end cell cell space space space space space space space space straight a end cell cell space space space space 4 straight a plus 3 straight b plus 2 straight c end cell row cell 3 straight a end cell cell space space space space space space space space 3 straight a end cell cell space space space space 10 straight a plus 6 straight b plus 3 straight c end cell end table close vertical bar space equals straight a cubed

Solution
Let space space increment space equals space open vertical bar table row straight a cell space space space space space space space space space space space space straight a plus straight b end cell cell space straight a plus straight b plus straight c end cell row cell 2 straight a end cell cell space space space space space space space space straight a end cell cell space space space space 4 straight a plus 3 straight b plus 2 straight c end cell row cell 3 straight a end cell cell space space space space space space space space 3 straight a end cell cell space space space space 10 straight a plus 6 straight b plus 3 straight c end cell end table close vertical bar space space space space space space space space space space space space space equals space space open vertical bar table row straight a cell space space space space straight a plus straight b end cell cell space space space space space straight a plus straight b plus straight c end cell row 0 straight a cell 2 straight a plus straight b end cell row 0 cell 3 straight a end cell cell 7 straight a plus 3 straight b end cell end table close vertical bar space comma space by space straight R subscript 2 space minus 2 straight R subscript 1 space comma space straight R subscript 3 minus 3 space straight R subscript 1 space space space space space space space space space space space space equals space straight a space open vertical bar table row straight a cell 2 straight a plus straight b end cell row cell 3 straight a end cell cell 7 straight a plus straight b end cell end table close vertical bar space comma space by space expanding space with space first space column space space space space space space space space space space space space equals space straight a space open square brackets table row cell 7 straight a squared plus 3 ab minus 6 straight a squared minus 3 ab space end cell end table close square brackets space equals straight a left parenthesis straight a squared space right parenthesis equals straight a cubed space

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