# romulo

Most popular questions and responses by romulo
1. ## discrete math

If a and b are positive integers, and m=lcm(a,b), explain why m divides any common multiple of a and b. The answer is in the definition of lcm:] the smallest multiple that is exactly divisible by every member of a set of numbers. So if m is divisble by a

2. ## discrete math

If a and b are positive integers, prove that; ab = gcd(a,b)*lcm(a,b).

3. ## discrete math

Prove by contradiction that for any even integer a and any odd integer b, 4 does not divide (a^2 + 2b^2). Proposition: That 4k (k is any integer) = a^2 +2b^2, and a is even, and b is odd. But 4k is even (product of any integer and 4), so a^2 must be even,

4. ## discrete math

If p is prime prove that p^1/2 (root p) is irrational. Generalize the proof that sqrt 2 is irrational. You can find several proofs here: http://www.cut-the-knot.org/proofs/sq_root.shtml You should be able to apply the proof to all square roots of prime

5. ## Linear Algebra

Let u and v be vectors in R^n, and let T be a linear operator on R^n. Prove that T(u) dot T(v) = u dot v IFF A^T = A^-1 where A is the standard matrix for T.