$If space straight A equals open square brackets table row 0 cell space space 6 end cell cell space 7 end cell row cell negative 6 end cell cell space space space 0 end cell cell space 8 end cell row 7 cell negative 8 end cell cell space 0 end cell end table close square brackets space comma space straight B equals open square brackets table row 0 cell space space 1 end cell cell space space 1 end cell row 1 cell space space 0 end cell cell space 2 end cell row 1 cell space space 2 end cell cell space 0 end cell end table close square brackets space comma space straight C equals open square brackets table row cell space space space space 2 end cell row cell negative 2 end cell row cell space space space 3 end cell end table close square brackets$
Calculate AC,BC and (A+B) C. Also, verify that (A+B) C-AC+BC.

Solution

straight A equals open square brackets table row 0 cell space space 6 space end cell cell space 7 end cell row cell negative 6 end cell cell space 0 end cell cell space 8 end cell row 7 cell negative 8 end cell cell space 0 end cell end table close square brackets space comma space straight B equals open square brackets table row 0 cell space 1 end cell cell space 1 end cell row 1 cell space 0 end cell cell space space 2 end cell row 1 cell space 2 end cell cell space 0 end cell end table close square brackets space comma space straight C equals open square brackets table row cell space space space 2 end cell row cell negative 2 end cell row cell space space space 3 end cell end table close square brackets straight A plus straight B equals open square brackets table row 0 cell space space 6 space end cell cell space 7 end cell row cell negative 6 end cell cell space 0 end cell cell space 8 end cell row 7 cell negative 8 end cell cell space 0 end cell end table close square brackets space open square brackets table row 0 cell space 1 end cell cell space 1 end cell row 1 cell space 0 end cell cell space space 2 end cell row 1 cell space 2 end cell cell space 0 end cell end table close square brackets space equals open square brackets table row 0 cell space space 7 end cell cell space 8 end cell row cell negative 5 end cell cell space space 0 end cell cell space 10 end cell row 8 cell negative 6 end cell cell space 0 end cell end table close square brackets therefore space left parenthesis straight A plus straight B right parenthesis straight C space equals space open square brackets table row 0 cell space space 7 end cell cell space 8 end cell row cell negative 5 end cell cell space space 0 end cell cell space 10 end cell row 8 cell negative 6 end cell cell space 0 end cell end table close square brackets space open square brackets table row cell space space space space 2 end cell row cell negative 2 end cell row cell space space space space 3 end cell end table close square brackets space equals space open square brackets table row cell 0 minus 14 plus 24 end cell row cell negative 10 plus 0 plus 30 end cell row cell 16 plus 12 plus 0 end cell end table close square brackets space equals open square brackets table row 10 row 20 row 28 end table close square brackets Again space space space space space space space AC equals open square brackets table row 0 cell space space 6 space end cell cell space 7 end cell row cell negative 6 end cell cell space 0 end cell cell space 8 end cell row 7 cell negative 8 end cell cell space 0 end cell end table close square brackets space open square brackets table row cell space space space 2 end cell row cell negative 2 end cell row cell space space space 3 end cell end table close square brackets space equals space open square brackets table row cell 0 minus 41 plus 21 end cell row cell negative 10 plus 0 plus 30 end cell row cell 16 plus 012 plus 0 end cell end table close square brackets space equals open square brackets table row 9 row 12 row 30 end table close square brackets AND space space space space space space space BC equals space open square brackets table row 0 cell space 1 end cell cell space 1 end cell row 1 cell space 0 end cell cell space 2 end cell row 1 cell space 2 end cell cell space 0 end cell end table close square brackets space open square brackets table row 2 row cell negative 2 end cell row 3 end table close square brackets space equals space open square brackets table row cell 0 space minus 2 space plus 3 end cell row cell 2 space plus 0 space plus 6 end cell row cell 2 space minus 4 space plus 0 end cell end table close square brackets space equals open square brackets table row cell space space 1 end cell row cell space space 8 end cell row cell negative 2 end cell end table close square brackets therefore space space space space space space AC plus BC equals open square brackets table row 9 row 12 row 30 end table close square brackets space plus open square brackets table row 1 row 8 row cell negative 2 end cell end table close square brackets space equals space open square brackets table row cell 9 plus 1 end cell row cell 12 plus 8 end cell row cell 30 minus 2 end cell end table close square brackets space equals open square brackets table row 10 row 20 row 28 end table close square brackets therefore space space space space space space left parenthesis straight A plus straight B right parenthesis straight C equals AC plus BC

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