Prove that for any natural n the number 3^(n+4)−3n is divisible by 16.

Step-by-step explanation:

Prove that for any natural number 3^(n+4)-3n is divisible by 16.

(I'm going to assume that you mean 3^(n+4)-3^n.)

1. We can break up 3^(n+4)-3n into 3^n * 3^4-3^n (by the rule a^b*a^c = a^b+c).

2. Solve to get 3^n * 81 - 3^n

3. Factor out the 3^n, and you'll get 3^n(81-1), and simplify: 3^n(80)

        You may notice that 80 is divisible by 16.

4. Rewrite what we got from the last step as: 3^n*5(16).

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step-by-step explanation:

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option (b) is correct

step-by-step explanation:

to find the solution of this system, we need to convert it into reduced row-echelon form. we have,

after applying row operations r2 -> r2/2 and r3 -> r3/3, we get,