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

Solution

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

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Question

Wired Faculty App

Evaluate

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

Solution

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

Question

Wired Faculty App

Evaluate
$open vertical bar table row 2 cell space space space space space space 4 end cell row cell negative 5 end cell cell space space space minus 1 end cell end table close vertical bar$

Solution

$Let space space space increment space equals space open vertical bar table row 2 cell space space space space space space 4 end cell row cell negative 5 end cell cell space space space minus 1 end cell end table close vertical bar space space space space space space space space space space space space space space equals space left parenthesis 2 right parenthesis space left parenthesis negative 1 right parenthesis minus left parenthesis negative 4 right parenthesis left parenthesis negative 5 right parenthesis space space space space space space space space space space space space space space equals space minus 2 plus 20 equals 18 space space space space space space$

Question

Wired Faculty App

Evaluate

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

Solution

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

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Determinants

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

Evaluate

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

Evaluate
$open vertical bar table row 2 cell space space space space space space 4 end cell row cell negative 5 end cell cell space space space minus 1 end cell end table close vertical bar$

Evaluate

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

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