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If f(x) = \begin{vmatrix} 1 & x& x+1\\ 2x & x(x-1)&x(x+1) \\ 3x(x-1) &x(x-1)(x-2) &x(x^2-1) \end{vmatrix} then f(100) is equal to

  • Option 1)

    0

  • Option 2)

    1

  • Option 3)

    100

  • Option 4)

    -100

 

Answers (1)

 

As we have learned

Property of determinant -

If two rows ( or two columns ) in a determinant have corresponding elements that are equal , the value of determinant is equal to zero 

-

 

 

 

f (x) = x.x.(x- 1) \begin{vmatrix} 1 &x & x+1\\ 2 & x-1& x+1\\ 3 & x-2 & x+1 \end{vmatrix}                       x2(x- 1) \begin{vmatrix} 1 &x &1 \\ 2 &x-1 &2 \\ 3& x-2 & 3 \end{vmatrix} = 0   

                        (C3\rightarrowC3- C2)

                        \therefore  f(100) = 0


Option 1)

0

Option 2)

1

Option 3)

100

Option 4)

-100

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subam

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