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Matrices

Question
CBSEENMA12034256
Wired Faculty App

Give example to show that 
  (A + B)2 = A2 + B2 + 2 AB.

Solution
Let space space straight A equals open square brackets table row 1 2 row cell negative 2 end cell 1 end table close square brackets space comma space straight B space equals space open square brackets table row 3 cell negative 4 end cell row 4 3 end table close square brackets therefore space space space straight A plus straight B space space equals space open square brackets table row cell 1 plus 3 end cell cell 2 minus 4 end cell row cell negative 2 plus 4 end cell cell 1 plus 3 end cell end table close square brackets space space equals space open square brackets table row 4 cell negative 2 end cell row 2 4 end table close square brackets therefore space space left parenthesis straight A plus straight B right parenthesis squared equals space open square brackets table row 4 cell negative 2 end cell row 2 4 end table close square brackets space open square brackets table row 4 cell negative 2 end cell row 2 4 end table close square brackets equals space open square brackets table row cell 16 minus 4 end cell cell negative 8 minus 8 end cell row cell 8 plus 8 end cell cell negative 4 plus 16 end cell end table close square brackets equals space open square brackets table row 12 cell negative 16 end cell row 16 12 end table close square brackets therefore space space left parenthesis straight A plus straight B right parenthesis squared equals open square brackets table row 12 cell negative 16 end cell row 16 12 end table close square brackets 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.... left parenthesis 1 right parenthesis space space space space space space space space space space space space space space straight A to the power of 2 space space end exponent equals space space open square brackets table row 1 2 row cell negative 2 end cell 1 end table close square brackets space open square brackets table row 1 2 row cell negative 2 end cell 1 end table close square brackets space equals open square brackets table row cell 1 minus 4 end cell cell 2 plus 2 end cell row cell negative 2 minus 2 end cell cell negative 4 plus 1 end cell end table close square brackets equals open square brackets table row cell negative 3 end cell 4 row cell negative 4 end cell cell negative 3 end cell end table close square brackets space space space space space space space space space space space space space space straight B squared space space space equals space open square brackets table row cell negative 3 end cell cell negative 4 end cell row cell negative 4 end cell cell negative 3 end cell end table close square brackets space space open square brackets table row cell negative 3 end cell cell negative 4 end cell row cell negative 4 end cell cell negative 3 end cell end table close square brackets space space space equals open square brackets table row cell 9 minus 16 end cell cell negative 12 minus 12 end cell row cell 12 plus 12 end cell cell negative 16 plus 9 end cell end table close square brackets equals open square brackets table row cell negative 7 end cell cell negative 24 end cell row 24 cell negative 7 end cell end table close square brackets space space space space space space space space space space space AB space space space space equals space open square brackets table row 1 2 row cell negative 2 end cell 1 end table close square brackets space space open square brackets table row cell negative 3 end cell cell negative 4 end cell row cell negative 4 end cell cell negative 3 end cell end table close square brackets space space equals space space open square brackets table row cell 3 plus 8 end cell cell negative 4 plus 6 end cell row cell negative 6 plus 4 end cell cell 8 plus 3 end cell end table close square brackets space equals open square brackets table row 11 2 row cell negative 2 end cell 11 end table close square brackets therefore space space space space 2 space AB space space equals open square brackets table row 22 4 row cell negative 4 end cell 22 end table close square brackets therefore space space space straight A squared space plus straight B squared plus 2 AB space equals space open square brackets table row cell negative 3 end cell 4 row cell negative 4 end cell cell negative 3 end cell end table close square brackets plus space open square brackets table row cell negative 7 end cell cell negative 24 end cell row 24 cell negative 7 end cell end table close square brackets plus space open square brackets table row 22 4 row cell negative 4 end cell 22 end table close square brackets 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 equals space space open square brackets table row cell negative 3 minus 7 plus 22 end cell cell 4 minus 24 plus 4 end cell row cell negative 4 plus 24 minus 4 end cell cell negative 3 minus 7 plus 22 end cell end table close square brackets therefore space space space straight A squared space plus straight B squared plus 2 AB space equals space open square brackets table row 12 cell negative 16 end cell row 16 12 end table close square brackets 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... left parenthesis 2 right parenthesis From space left parenthesis 1 right parenthesis space and space left parenthesis 2 right parenthesis comma space we space get comma left parenthesis straight A space plus space straight B right parenthesis squared space equals space straight A squared space plus space straight B to the power of 2 space end exponent plus space 2 space AB.

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