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Determinants

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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