romulo
Most popular questions and responses by romulo
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
asked on March 7, 2007 
discrete math
If a and b are positive integers, prove that; ab = gcd(a,b)*lcm(a,b).
asked on March 7, 2007 
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,
asked on March 7, 2007 
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.cuttheknot.org/proofs/sq_root.shtml You should be able to apply the proof to all square roots of prime
asked on March 7, 2007 
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.
asked on March 7, 2007 
Linear Alebra
Find the eigenvalues and eigenvectors for the standard matrix : { 1 2 0} {2 1 1} {0 0 1}
asked on March 7, 2007

math
V=120x44x2+4x3
posted on July 9, 2011