Question

Evaluate the following determinants :

$open square brackets table row 12 cell space space 3 end cell cell space space 7 end cell row 13 cell space space 17 end cell cell space space 5 end cell row 15 cell space space 20 end cell cell space 12 end cell end table close square brackets squared$

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Solution

Let space space increment space equals space space open vertical bar table row 2 cell space 3 end cell cell space space 7 end cell row 13 cell space space 17 end cell cell space space 5 end cell row 15 cell space space 20 end cell cell space space 12 end cell end table close vertical bar space equals 2 space open vertical bar table row 17 cell space space space space space 5 end cell row 20 cell space space space space space 12 end cell end table close vertical bar space minus 3 space open vertical bar table row 13 cell space space 5 end cell row 15 cell space space 12 end cell end table close vertical bar plus 7 space open vertical bar table row 13 cell space space 17 end cell row 15 cell space space 20 end cell end table close vertical bar space space space space space space space space space space space space equals 2 left parenthesis left parenthesis 204 minus 100 right parenthesis minus 3 left parenthesis 156 minus 175 right parenthesis plus 7 left parenthesis 260 minus 255 right parenthesis equals 208 space minus 243 plus 35 equals 0 space space space space space increment squared space equals space space open vertical bar table row 2 cell space 3 end cell cell space space 7 end cell row 13 cell space space 17 end cell cell space space 5 end cell row 15 cell space space 20 end cell cell space space 12 end cell end table close vertical bar space equals 0

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