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Sponsor Area

Determinants

Question
CBSEENMA12034391
Wired Faculty App

Using space properties space of space determinants comma space prove space that open vertical bar table row cell straight y plus straight z end cell straight z cell space space straight y end cell row straight z cell space space straight z plus straight x end cell cell space space straight x end cell row straight y straight x cell space space space straight x plus straight y end cell end table close vertical bar space equals 4 xyz

Solution
Let space space increment space equals open vertical bar table row cell straight y plus straight z end cell straight z cell space space straight y end cell row straight z cell space space straight z plus straight x end cell cell space space straight x end cell row straight y straight x cell space space space straight x plus straight y end cell end table close vertical bar space space space space space space space space space space space space equals space space open vertical bar table row cell 2 left parenthesis straight y plus straight z right parenthesis end cell cell space space 2 left parenthesis straight z plus straight x right parenthesis space space end cell cell 2 left parenthesis straight x plus straight y right parenthesis end cell row straight z cell straight z plus straight x end cell straight x row straight y straight x cell straight x plus straight y end cell end table close vertical bar space space comma space by space straight R subscript 1 space plus straight R subscript 2 space end subscript plus straight R subscript 3 space space space space space space space space space space space equals space 2 space open vertical bar table row cell straight y plus straight z end cell cell space space straight z plus straight x end cell cell space space straight x plus straight y end cell row straight z cell space space straight z plus straight x end cell straight x row straight y straight x cell space straight x plus straight y end cell end table close vertical bar space equals 2 space open vertical bar table row straight y cell space space 0 end cell straight y row straight z cell space space space straight z plus straight x end cell straight x row straight y straight x cell space space straight x plus straight y end cell end table close vertical bar space comma space by space straight R subscript 1 space minus straight R subscript 2 space end subscript space space space space space space space space space space space equals space 2 space space open vertical bar table row straight y 0 0 row straight z cell space space space space straight z plus straight x end cell cell space space straight x minus straight z end cell row straight y straight x straight x end table close vertical bar space comma space by space straight C subscript 3 space minus straight C subscript 1 space space space space space space space space space space space equals space 2 straight y space open vertical bar table row cell straight z plus straight x end cell cell space space space straight x minus straight z end cell row straight x straight x end table close vertical bar space equals 2 straight y space open square brackets table row cell straight x left parenthesis straight z plus straight x right parenthesis minus straight x left parenthesis straight x minus straight z right parenthesis end cell end table close square brackets space space space space space space space space space space equals space 2 xy space open square brackets table row cell left parenthesis straight z plus straight x right parenthesis minus left parenthesis straight x minus straight z right parenthesis end cell end table close square brackets space equals 2 xy space open square brackets table row cell straight z plus straight x minus straight x plus straight z end cell end table close square brackets space space space space space space space space space space equals space 2 xy space cross times space 2 straight z space equals 4 xyz

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