Important Questions of Determinants Mathematics | Zigya
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    Mathematics : Determinants

    Multiple Choice QuestionsShort Answer Type

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    71. If space straight a comma space straight b comma space straight c space are space positive space and space unequal comma space show space that space value space of space the space determinant increment space space equals space open vertical bar table row straight a cell space space space straight b end cell cell space space space space straight c end cell row straight b cell space space space straight c end cell cell space space space space straight a end cell row straight c cell space space space straight a end cell cell space space space space straight b end cell end table close vertical bar space is space negative.
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    72. prove space that space open vertical bar table row cell negative straight a end cell cell space space ab end cell cell space space ac end cell row ba cell space space minus straight b squared end cell cell space space space bc end cell row ca cell space cb end cell cell negative straight c squared end cell end table close vertical bar space equals 4 space straight a to the power of 2 space end exponent straight b squared space straight c squared
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    73. Evaluate space open vertical bar table row 0 cell space space space ab squared end cell cell space space ac squared end cell row cell straight a squared space straight b end cell 0 cell space bc squared end cell row cell straight a squared straight c end cell cell space space straight b squared space straight c end cell cell space 0 end cell end table close vertical bar
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    74. Evaluate open vertical bar table row cell straight x plus straight lambda end cell straight x straight x row straight x cell space space straight x plus straight lambda end cell straight x row straight x straight x cell space space straight x plus straight lambda end cell end table close vertical bar
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    75. Evalute space space open vertical bar table row cell straight b plus straight c end cell straight a straight a row straight b cell space space space space straight c plus straight a end cell straight b row straight c straight c cell space space straight a plus straight b end cell end table close vertical bar
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    76.

    show that
    open vertical bar table row 1 cell space space space space straight x end cell cell space space space space straight x squared end cell row cell straight x squared end cell cell space space 1 end cell cell space space straight x end cell row straight x cell space space straight x squared end cell cell space space 1 end cell end table close vertical bar space equals space left parenthesis 1 minus x cubed right parenthesis squared

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    77. Using space properties space of space determinants comma space prove space that space open vertical bar table row cell straight y plus straight z end cell cell space space space straight x end cell cell space space straight y end cell row cell straight z plus straight x end cell cell space space straight z end cell cell space space straight x end cell row cell straight x plus straight y end cell cell space space straight y end cell cell space straight z end cell end table close vertical bar space equals space left parenthesis straight x plus straight y plus straight z right parenthesis space left parenthesis straight x minus straight z right parenthesis squared
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    78. Using space properties space of space determinants comma space prove space that open vertical bar table row cell straight y plus straight z end cell straight z cell space space straight y end cell row straight z cell space space straight z plus straight x end cell cell space space straight x end cell row straight y straight x cell space space space straight x plus straight y end cell end table close vertical bar space equals 4 xyz
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    79. show space that open vertical bar table row straight a cell space space space space space space space space space straight a plus straight b end cell cell straight a plus straight b plus straight c end cell row cell 2 straight a end cell cell space space space space space space space space 3 straight a plus 2 straight b end cell cell space space 4 straight a plus 3 straight b plus 2 straight c end cell row cell 3 straight a end cell cell space space space space space 6 straight a plus straight b end cell cell space space space space space 10 straight a plus 6 straight b plus 3 straight c end cell end table close vertical bar space equals straight a cubed
    98 Views
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    80.

    Show thatopen vertical bar table row cell straight a plus straight b plus 2 straight c end cell straight a straight b row straight c cell space space space space space straight b plus straight c plus 2 straight a end cell straight b row straight c straight a cell space space straight c plus straight a plus 2 straight b end cell end table close vertical bar

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