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

    Previous Year Papers

    Download Solved Question Papers Free for Offline Practice and view Solutions Online.

    Test Series

    Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

    Test Yourself

    Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.
    Advertisement

    Matrices

    Multiple Choice QuestionsShort Answer Type

    131.  Give example to show that .
       AB = O = BA where A ≠ O, B ≠ O
    96 Views
    Answer
    132. Give example to show that .
     AB = AC but B ≠ C.
    88 Views
    Answer
    Advertisement
    Zigya App

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

    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.
    75 Views
  • Switch Icon Switch
    • Advertisement
    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.
    73 Views
    Answer
    Advertisement
    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.
    73 Views
    Answer
    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.
    86 Views
    Answer
    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
    76 Views
    Answer
    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
    74 Views
    Answer
    Advertisement
    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
    73 Views
    Answer
    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
    74 Views
    Answer
    Advertisement
    Flag Popup Icon
    Flag it
    Submit
    Flag Popup Icon
    Switch to
    flexipad
    Share It Icon
    Share it
    Share It
    Share it