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Determinants

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Mathematics Part I

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Mathematics

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CBSE Gujarat Board Haryana Board

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Class 10 Class 12

Determinants

Evaluates :

open vertical bar table row cell sin space 30 degree end cell cell space space cos space 30 degree end cell row cell negative sin space 60 degree end cell cell space cos space 60 degree end cell end table close vertical bar

Let space space increment space equals space open vertical bar table row cell sin space 30 degree end cell cell space space cos space 30 degree end cell row cell negative sin space 60 degree end cell cell space cos space 60 degree end cell end table close vertical bar space space space space space space space space space space space space equals space sin space 30 degree space cos space 60 degree space space plus space cos space 30 degree space space sin space 60 degree space equals space sin space left parenthesis 30 degree space plus 60 degree right parenthesis space space space space space space space space space space space space equals space sin space 90 degree space equals 1

107 Views

Evaluates :
$open vertical bar table row cell straight a plus ib end cell cell straight c plus id end cell row cell negative straight c plus ic end cell cell straight a minus ib end cell end table close vertical bar$

open vertical bar table row cell straight a plus ib end cell cell straight c plus id end cell row cell negative straight c plus ic end cell cell straight a minus ib end cell end table close vertical bar space equals space left parenthesis straight a plus ib right parenthesis left parenthesis straight a minus ib right parenthesis minus left parenthesis straight c plus id right parenthesis left parenthesis straight c minus id right parenthesis space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space left parenthesis straight a squared minus straight i squared straight b squared right parenthesis minus left parenthesis straight i squared space straight d to the power of 2 space space end exponent minus straight c squared right parenthesis space space space space space space space space space space space space space space space space space space space space space space space space space open square brackets table row because cell straight i squared space equals space minus 1 end cell end table close square brackets space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space left parenthesis straight a squared plus straight b squared right parenthesis space minus left parenthesis negative straight d squared minus straight c squared right parenthesis space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals straight a squared plus straight b squared space plus straight c to the power of 2 space end exponent plus straight d squared space space space space space space space space space space space space

325 Views

Evaluates :

open vertical bar table row cell 2 space cos space straight theta space space end cell cell negative 2 space sin space straight theta end cell row cell sin space straight theta end cell cell cos space straight theta end cell end table close vertical bar

Let space space space increment space space equals space open vertical bar table row cell 2 cos space straight theta space space end cell cell negative 2 sin space straight theta end cell row cell sin space straight theta end cell cell cos space straight theta end cell end table close vertical bar space space space space space space space space space space space space space space space equals space left parenthesis 2 cos space straight theta right parenthesis left parenthesis cos space straight theta right parenthesis minus left parenthesis negative 2 sin space straight theta right parenthesis left parenthesis sin space straight theta right parenthesis equals 2 cos squared straight theta space plus 2 space 2 sin squared space straight theta space space space space space space space space space space space space space space space space space space space equals space 2 space left parenthesis cos squared space straight theta space plus space sin squared space straight theta right parenthesis equals 2 left parenthesis 1 right parenthesis equals 2

141 Views

Evaluate

open vertical bar table row straight x cell straight x plus 1 end cell row cell straight x minus 1 end cell straight x end table close vertical bar

Let space space space increment space equals space open vertical bar table row straight x cell straight x plus 1 end cell row cell straight x minus 1 end cell straight x end table close vertical bar space space space space space space space space space space space space space space equals space left parenthesis straight x right parenthesis space left parenthesis straight x right parenthesis minus left parenthesis straight x plus 1 right parenthesis left parenthesis straight x minus 1 right parenthesis space equals space straight x squared space minus left parenthesis straight x to the power of 2 space end exponent minus 1 right parenthesis equals straight x squared space minus straight x squared plus 1 equals 1 space

129 Views

Evaluate

open vertical bar table row 2 cell space 4 end cell row cell negative 1 end cell cell space 2 end cell end table close vertical bar

Let space space space space space space increment equals space open vertical bar table row 2 cell space 4 end cell row cell negative 1 end cell cell 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 left parenthesis 2 right parenthesis space left parenthesis 2 right parenthesis minus left parenthesis 4 right parenthesis left parenthesis negative 1 right parenthesis equals 4 plus 4 equals 8

134 Views