Matrix f ( x ) has Row 1: 1, x , 0 ; Row 2: 0 , 1 , 0 ; Row 3: 0 , 0 , 1 . For n ∈ N , ( f ( x ) ) n equals

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Matrix $f (x)$ has Row 1: 1, $x, 0$ ; Row 2: $0, 1, 0$ ; Row 3: $0, 0, 1$ . For $n \in N, (f (x))^{n}$ equals

Answer:

Solution:

Write $f (x) = I + B$ with $B^{2} = 0$ . Then $(I + B)^{n} = I + n B = f (n x)$ .

Stream:JEESubject:MathematicsTopic:MatricesSubtopic:Product of Matrices

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