1.

If `f(x) = |(x + lamda,x,x),(x,x + lamda,x),(x,x,x + lamda)|, " then " f(3x) - f(x) =`A. `3x lamda^(2)`B. `6x lamda^(2)`C. `x lamda^(2)`D. none of these

Answer» Correct Answer - B
We have,
`f(x) = |(x + lamda,x,x),(x,x + lamda,x),(x,x,x + lamda)|`
`rArr f(x) |(3x + lamda,x,x),(3x + lamda,x + lamda,x),(3x + lamda,x,x + lamda)| " " [(" Applying "),(C_(1) rarr C_(1) + C_(2) + C_(3))]`
`rArr f(x) = (3x + lamda) |(1,x,x),(1,x + lamda,x),(1,x,x + lamda)|`
`rArr f(x) = (3x + lamda) |(1,x,x),(0,lamda,0),(0,0,lamda)| " " [("Applying " R_(2) rarr R_(2) - R_(1)),(" "R_(3) rarr R_(3) - R_(1))]`
`rArr f(x) = (3x + lamda) lamda^(2)`
`:. f(3x) - f(x) = (9x + lamda) lamda^(2) - (3x + lamda) lamda^(2) = 6x lamda^(2)`


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