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Determinants

Question
CBSEENMA12034352
Wired Faculty App

If any two rows of a determinant are interchanged, then sign of determinant verify space this space property space for space increment space equals space open vertical bar table row 2 cell space space minus 3 end cell cell space space space space space space 5 end cell row 6 cell space space space space space 0 end cell cell space space space space space space 4 end cell row 1 cell space space space space 5 end cell cell space space minus 7 end cell end table close vertical barchanges.

Solution
increment space equals space open vertical bar table row 2 cell space space minus 3 end cell cell space space space space space space 5 end cell row 6 cell space space space space space 0 end cell cell space space space space space space 4 end cell row 1 cell space space space space 5 end cell cell space space minus 7 end cell end table close vertical bar increment space equals space 2 space open vertical bar table row 0 cell space space space space 4 end cell row 5 cell space space minus 7 end cell end table close vertical bar space minus left parenthesis negative 3 right parenthesis space open square brackets table row 6 cell space space space space space 4 end cell row 1 cell space space minus 7 end cell end table close square brackets space plus 5 space open square brackets table row 6 cell space space 0 end cell row 1 cell space space 5 end cell end table close square brackets space space space space space equals space 2 space left parenthesis 0 minus 20 right parenthesis plus 3 left parenthesis negative 42 minus 4 right parenthesis plus 5 left parenthesis 30 minus 0 right parenthesis equals negative 40 minus 138 plus 150 equals negative 28 Interchanging space rows space straight R 2 space and space straight R 3 space straight i. straight e. space straight R 2 space left right arrow space straight R 3 comma space we space have space increment subscript 1 space space end subscript equals space open vertical bar table row 2 cell space space space minus 3 end cell cell space space space space space space 5 end cell row 1 cell space space space space space space 5 end cell cell space space space space space minus 7 end cell row 6 cell space space space space space 0 end cell cell space space space space space space 4 end cell end table close vertical bar increment subscript 1 space space end subscript equals space space 2 space open vertical bar table row 5 cell space space space minus 7 end cell row 0 cell space space space space space space 4 end cell end table close vertical bar plus 3 space open square brackets table row 1 cell space space space space minus 7 end cell row 6 cell space space space space space space space space space 4 end cell end table close square brackets space plus 5 space open square brackets table row 1 cell space space space 5 end cell row 6 cell space space 0 end cell end table close square brackets space space space space space space space equals space space 2 left parenthesis 20 minus 0 right parenthesis plus 3 left parenthesis 4 plus 42 right parenthesis plus 5 left parenthesis 0 minus 30 right parenthesis equals 40 plus 138 minus 150 equals 28 therefore space space space increment subscript 1 space space end subscript equals space minus increment therefore space space property space is space verified

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