f(x)=x+λxxxx+λxxxx+λthen f(3x)−f(x)= - Sri Chaitanya Infinity Learn Best Online Courses for NCERT Solutions, CBSE, ICSE, JEE, NEET, Olympiad and Class 6 to 12

A
$3 {xλ}^{2}$
B
$6 {xλ}^{2}$
C
${xλ}^{2}$
D
$9 {xλ}^{2}$

Solution:

Apply $\begin{array}{l} R_{1} \to R_{1} - R_{2} \\ R_{2} \to R_{2} - R_{3} \end{array}\} = |\begin{matrix} x + λ & x & x \\ x & x + λ & x \\ x & x & x + λ \end{matrix}| = |\begin{matrix} λ & - λ & 0 \\ 0 & λ & - λ \\ x & x & x + λ \end{matrix}| = λ (λ x + λ^{2} + λ x) + λ (0 + λ x) = f (x) = 3 λ^{2} x + λ^{3}$
$∴ f (3 x) - f (x) = 6 λ^{2} x$

$f (x)$ $= |\begin{matrix} x + λ & x & x \\ x & x + λ & x \\ x & x & x + λ \end{matrix}|$ then $f (3 x) - f (x) =$

Solution:

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