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Question

IF A=[1413]andB=[1211] Find
(i)(A+B)2 (ii) A2+B2
(iii) Is (A + B)^2 = A^2+ B^2?\)


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    Solution

    left parenthesis i right parenthesis A plus B equals open square brackets table row 1 4 row 1 cell negative 3 end cell end table close square brackets plus open square brackets table row 1 2 row cell negative 1 end cell cell negative 1 end cell end table close square brackets equals open square brackets table row 2 6 row 0 cell negative 4 end cell end table close square brackets left parenthesis A plus B right parenthesis squared equals open square brackets table row 2 6 row 0 cell negative 4 end cell end table close square brackets open square brackets table row 2 6 row 0 cell negative 4 end cell end table close square brackets space space space space space space space space space space space space space space equals open square brackets table row cell 4 plus 0 end cell cell 12 minus 24 end cell row cell 0 plus 0 end cell cell 0 plus 16 end cell end table close square brackets space space space space space space space space space space space space space space equals open square brackets table row 4 cell negative 12 end cell row 0 16 end table close square brackets left parenthesis i i right parenthesis A squared equals open square brackets table row 1 4 row 1 cell negative 3 end cell end table close square brackets open square brackets table row 1 4 row 1 cell negative 3 end cell end table close square brackets space space space space space equals open square brackets table row cell 1 plus 4 end cell cell 4 minus 12 end cell row cell 1 minus 3 end cell cell 4 plus 9 end cell end table close square brackets space space space space space equals space open square brackets table row 5 cell negative 8 end cell row cell negative 2 end cell 13 end table close square brackets B squared equals open square brackets table row 1 2 row cell negative 1 end cell cell negative 1 end cell end table close square brackets open square brackets table row 1 2 row cell negative 1 end cell cell negative 1 end cell end table close square brackets space space space space space equals open square brackets table row cell 1 minus 2 end cell cell 2 minus 2 end cell row cell negative 1 plus 1 end cell cell negative 2 plus 1 end cell end table close square brackets space space space space space equals open square brackets table row cell negative 1 end cell 0 row 0 cell negative 1 end cell end table close square brackets A squared plus B squared equals open square brackets table row 5 cell negative 8 end cell row cell negative 2 end cell 13 end table close square brackets plus open square brackets table row cell negative 1 end cell 0 row 0 cell negative 1 end cell end table close square brackets space space space space space space space space space space space space space space equals open square brackets table row 4 cell negative 8 end cell row cell negative 2 end cell 12 end table close square brackets left parenthesis i i i right parenthesis C l e a r l y space left parenthesis A plus B right parenthesis squared not equal to A squared plus B squared

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