Matrices and Determinants 2 Question 16
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18. If $f(x)=\begin{array}{ccc}1 & x & x+1 \ 2 x & x(x-1) & (x+1) x \ 3 x(x-1) & x(x-1)(x-2) & (x+1) x(x-1)\end{array}$,
======= ####18. If $f(x)=\begin{vmatrix}1 & x & x+1 \\ 2 x & x(x-1) & (x+1) x \\ 3 x(x-1) & x(x-1)(x-2) & (x+1) x(x-1)\end{vmatrix}$,
3e0f7ab6f6a50373c3f2dbda6ca2533482a77bed
then $f(100)$ is equal to
(1999, 2M)
(a) 0
(b) 1
(c) 100
(d) -100
Show Answer
Answer:
Correct Answer: 18. (a)
Solution:
- Given,
$ f(x)=\begin{vmatrix} 1 & x & x+1 \\ 2 x & x(x-1) & (x+1) x \\ 3 x(x-1) & x(x-1)(x-2) & (x+1) x(x-1) \end{vmatrix} $
Applying $C _3 \rightarrow C _3-\left(C _1+C _2\right)$
$ \begin{vmatrix} 1 & x & 0 \\ 2 x & x(x-1) & 0 \\ 3 x(x-1) & x(x-1)(x-2) & 0 \end{vmatrix} $
$ \therefore \quad f(x)=0 \Rightarrow f(100)=0 $
