Recent content by bronxbombas

Homework Statement Let A, B, C, D be the vertices of a convex quadrilateral. Convexity means that for each lines L(ab), L(bc), L(cd), L(da) the quadrilateral lies in one of its half-planes. Find the point P for which the minimum Min(d(P,A)+d(P,B)+d(P,C)+d(P,D)) is realized. Homework...

Homework Statement Prove that if A is an invertible matrix, then A*AT and AT*A are also invertible. Homework Equations (AT)-1=(A-1)T (AB)T=ATBT The Attempt at a Solution I just can't wrap my brain around this one. I know that I have to multiply a matrix by its inverse to get the...

I also have another problem that takes priority over this one if anybody can help. Prove that (2n)!/(2^n*n!) is an odd number when n is a nonnegative integer.

Homework Statement Suppose that gcd(a,b)=1 and that a|n and b|n. Prove that ab|n. Homework Equations Since we know that gcd(a,b)=1, we can say that ax+by=1 for some x,y as elements of the integer set. The Attempt at a Solution My professor said I should multiply the entire...

I understand the example you give for E. For C, I don't get how that can be false. How can the function be discontinuous if it's from R to R? I understand why arctan doesn't work for D. So is it safe to assume that one's true?

I got some more. I'd appreciate some feedback. C. Every injective function from R to R is monotone. I think this one's true. D. Every surjective function from R to R is unbounded. Would arctan(x) disprove this one? I'm not sure if surjection is limited to the range of a function or for...

do you mean something like y=5 would work?

Homework Statement Determine which of the following statements are true. Give proofs for the true statements and counterexamples for the false statements. Homework Equations B. Every non-decreasing function from R to R is injective. The Attempt at a Solution So I think I know a...