Question

6) Cramer’s Rule

Solve each using Cramer’s rule

a) 3x + .5y =10

      10x -    -y = -3

b) x + z +y = 12

-x + 3y - z = 2

     -2x + z = -2

7) Proofs

Prove the following by induction

    1. n³ – n is divisible by 3 for n >=2

    2. . Prove that n! < n^{n for}n ≥ 2.

Prove directly that:

The sum of an integer and its cube is even.

Answer 1

ANSWER 7 (2)

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