Question

Show that:
$open vertical bar table row straight a cell space space straight b end cell cell space space straight c end cell row cell straight a plus 2 straight x end cell cell space straight b plus 2 straight y end cell cell space space space straight c plus 2 space straight z end cell row straight x straight y cell space straight z end cell end table close vertical bar space equals space 0$

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Solution

straight L. straight H. straight S. space equals space open vertical bar table row straight a cell space space straight b end cell cell space space straight c end cell row cell straight a plus 2 straight x end cell cell space space straight b plus 2 straight y end cell cell space space space straight c plus 2 straight z end cell row straight x straight y straight z end table close vertical bar space space space space space space space space space space space space equals space open vertical bar table row straight a cell space space space straight b end cell cell space space straight c end cell row straight a cell space space straight b end cell cell space space straight c end cell row straight x cell space space straight y end cell cell space space straight z end cell end table close vertical bar space plus space open vertical bar table row straight a straight b straight c row cell 2 space straight x end cell cell 2 space straight y end cell cell 2 space straight z end cell row straight x straight y straight z end table close vertical bar equals space open vertical bar table row straight a cell space space straight b end cell cell space space straight c end cell row straight a cell space space straight b end cell cell space space straight c end cell row straight x cell space space straight y end cell cell space space straight z end cell end table close vertical bar plus space 2 space open vertical bar table row straight a cell space space straight b end cell cell space space straight c end cell row straight x cell space space straight y end cell cell space space straight z end cell row straight x cell space space straight y end cell cell space space straight z end cell end table close vertical bar equals space 0 plus 2 space left parenthesis 0 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 space space space space space space space space space space space space space space space space space space open square brackets because two space rows space are space identical close square brackets space equals space 0 plus 0 space equals space 0 space equals space straight R. straight H. straight S.

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