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    Matrices

    Multiple Choice QuestionsShort Answer Type

    131.  Give example to show that .
       AB = O = BA where A ≠ O, B ≠ O
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    132. Give example to show that .
     AB = AC but B ≠ C.
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    133. Give example to show that 
      (A + B)2 = A2 + B2 + 2 AB.
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    134. If space straight A equals open square brackets table row 1 2 row 2 1 end table close square brackets comma space then space show space that space space space straight A squared space – space 3 space straight I space equals space 2 straight A.
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    135. If space space straight A equals open square brackets table row 2 3 row 1 cell 2 space end cell end table close square brackets comma space prove space that space straight A to the power of 1 space — space 4 straight A squared space plus space straight A space equals space straight O.
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    136. If space space space straight A equals space open square brackets table row 3 1 row cell negative 1 end cell 2 end table close square brackets,  verify that A2 — 5A + 71 = O.
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    137. If space straight A equals space open square brackets table row 3 cell negative 5 end cell row cell negative 4 end cell 2 end table close square brackets space comma Show that straight A squared minus 5 straight A minus 141 equals 0

    Here space space straight A equals space open square brackets table row 3 cell negative 5 end cell row cell negative 4 end cell 2 end table close square brackets straight A squared equals straight A. straight A equals space space open square brackets table row 3 cell negative 5 end cell row cell negative 4 end cell 2 end table close square brackets space open square brackets table row 3 cell negative 5 end cell row cell negative 4 end cell 2 end table close square brackets space space space space space space space space space space space space space space space space space equals space open square brackets table row cell 9 plus 20 end cell cell negative 15 minus 10 end cell row cell negative 12 minus 8 end cell cell 20 plus 4 end cell end table close square brackets equals space open square brackets table row 29 cell negative 25 end cell row cell negative 20 end cell 24 end table close square brackets space space space space space space straight L. straight H. straight S space equals space straight A squared space minus 5 straight A minus 141 space space space space space space space space space space space space space space space space space equals space open square brackets table row 29 cell negative 25 end cell row cell negative 20 end cell 24 end table close square brackets space minus 5 space open square brackets table row 3 cell negative 5 end cell row cell negative 4 end cell 2 end table close square brackets minus 14 space open square brackets table row 1 0 row 0 1 end table close square brackets space space space space space space space space space space space space space space space space space equals space open square brackets table row 29 cell negative 25 end cell row cell negative 20 end cell 24 end table close square brackets space plus space open square brackets table row cell negative 15 end cell 25 row 20 cell negative 10 end cell end table close square brackets space plus space open square brackets table row cell negative 14 end cell 0 row 0 cell negative 14 end cell end table close square brackets space space space space space space space space space space space space space space space space space space space equals space open square brackets table row cell 29 minus 15 minus 14 end cell cell negative 25 plus 25 plus 0 end cell row cell negative 20 plus 20 plus 0 end cell cell 24 minus 10 minus 14 end cell end table close square brackets space equals space straight O space space space space space space space space space space space space space space space space space space equals space space space space space space straight R. straight H. straight S space space space space space space space space space space space space space space space
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    138. If space straight A equals space space open square brackets table row 3 cell space space space 2 end cell cell space space 0 end cell row 1 cell space space 4 end cell cell space space 0 end cell row 0 cell space space space 0 space end cell 5 end table close square brackets space comma space show space that space straight A squared space minus 7 straight A space plus space 10 space straight I subscript 3 space end subscript equals space 0
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    139. Find space straight A squared space minus 5 straight A plus 6 space straight I space If space straight A space equals space open square brackets table row 2 0 1 row 2 1 3 row 1 cell negative 1 end cell 0 end table close square brackets
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    140. If space straight A equals space open square brackets table row 1 2 row 2 1 end table close square brackets space comma space straight f space left parenthesis straight x right parenthesis space equals straight x to the power of 2 space end exponent minus 2 straight x minus 3 space show space that space straight f left parenthesis straight A right parenthesis equals straight O
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