If `f(x)= |{:(1,,x,,x+1),(2x,,x(x-1),,(x+1)x),(3x(x-1),,x(x-1)(x-2),,(x+1)x(x-1)):}|` then the value of f(500) `"_____"`

Answer

0

Explanation

Taking x common from `R_(2) " and " x(x-1)` common from`R_(3)` we get
`f(x) =x^(2) (x-1) |{:(1,,x,,x+1),(2,,x-1,,x+1),(3,,x-2,,x+1):}|`
Applying `C_(3) to C_(3)-C_(2)` we get
`f(x) =x^(2) (x-1) |{:(1,,x,,1),(2,,x-1,,2),(3,,x-2,,3):}|=0`
Thus `f(500) =0 `