RolyPoly
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Questions Asked

RolyPoly:
Group Title
Given \(\mathbb{F}\) is an ordered field, prove 1>0.
 updated 19 days ago
 15 replies
 No Medals Yet
Mathematics

RolyPoly:
Group Title
There is a line "And I think to myself what a wonderful world" in the song What a Wonderful World by Louis Armstrong. My question is, what i…
 updated 2 months ago
 1 reply
 No Medals Yet
Mathematics

RolyPoly:
Group Title
Let A and B be square matrices of the same size. If A and B are both ______, so is AB.
1) symmetric
2) invertible
…
 updated 4 months ago
 31 replies
 1 Medal
Mathematics

RolyPoly:
Group Title
Let A be a 4x7 matrix with rank 4. Which of the following(s) is/are true?
1) the rows of A are linearly independent
2) the columns of A mu…
 updated 4 months ago
 12 replies
 1 Medal
Mathematics

RolyPoly:
Group Title
Find the range of the function \(f(x) = x^\frac{1}{x}\)
 updated 5 months ago
 11 replies
 7 Medals
Mathematics

RolyPoly:
Group Title
Is this statement true?
"If U, W are subspaces of \(\mathbb{R}^n\) and dim U + dim W = n, then \(U\cap W = {0}\)"
 updated 5 months ago
 3 replies
 2 Medals
Mathematics

RolyPoly:
Group Title
Given A and B are subspaces of \(\mathbb{R}^n\). Is A+B a subspace of \(\mathbb{R}^n\) in general, given that A+B = {\(\vec{a} + \vec{b}  \…
 updated 5 months ago
 No Medals Yet
Mathematics

RolyPoly:
Group Title
What can you tell about the eigenvalues of matrix \(A^2\) if an eigenvalue of matrix \(A\) is \(\lambda\) and the corresponding eigenvector…
 updated 5 months ago
 1 reply
 No Medals Yet
Mathematics

RolyPoly:
Group Title
The number of passengers of terminal A, A(n) and terminal B, B(n), in the nth year are \(A(n)=2pq^n\) and \(B(n) = npq^2\), where p and q ar…
 updated 5 months ago
 33 replies
 3 Medals
Mathematics

RolyPoly:
Group Title
A student committee consists of 20 boys and 15 girls. A team of 8 students is selected randomly from the committee to participate in an acti…
 updated 6 months ago
 33 replies
 3 Medals
Mathematics

RolyPoly:
Group Title
Why do we use radian instead of degree in "higher mathematics", for example, in calculus?
 updated 6 months ago
 9 replies
 No Medals Yet
Mathematics

RolyPoly:
Group Title
It is known that a system has infinitely many solutions.
What happens when such a real system has a unique solution?
 updated 6 months ago
 No Medals Yet
Mathematics

RolyPoly:
Group Title
Given an undirected graph H, let C be the adjacency matrix of H. What is the meaning of entries in \(C^n\)?
 updated 6 months ago
 20 replies
 2 Medals
Mathematics

RolyPoly:
Group Title
Write a recursive algorithm S(C,D,m,n) with the following requirements:
1) C is an array with m elements stored in positions C[1,...,m]
2)…
 updated 7 months ago
 13 replies
 No Medals Yet
Mathematics

RolyPoly:
Group Title
Use MI to prove that \(n^21\) is divisible by 8 for any positive odd integer n.
 updated 7 months ago
 8 replies
 1 Medal
Mathematics

RolyPoly:
Group Title
Solve the following recurrence:
\[f(x) =\begin{cases} x & x \le 3 \\ f(x3) + 4 & x > 3\end{cases}\]
 updated 7 months ago
 76 replies
 2 Medals
Mathematics

RolyPoly:
Group Title
<Linear Algebra>
Prove that a system of linear equations cannot have exactly two solutions.
 updated 6 months ago
 23 replies
 2 Medals
Mathematics

RolyPoly:
Group Title
<Linear Algebra>
In the process of solving a system of linear equations, we have three elementary row operations, which are
(I) Exchange t…
 updated 7 months ago
 39 replies
 3 Medals
Mathematics

RolyPoly:
Group Title
Consider f(n) = lg(n).
What is the largest size n of the problem that can be solved in 1 second, assuming that the time required to solve t…
 updated 8 months ago
 82 replies
 1 Medal
Mathematics

RolyPoly:
Group Title
Whether zero is a natural number or not is still controversial.
What is the (mathematical) argument for 0 *NOT* being a natural number?
 updated 8 months ago
 8 replies
 1 Medal
Mathematics

RolyPoly:
Group Title
"The numbers 1, 1+1=2, 2+1=3, etc. are said to be natural; it is assumed that none of these numbers is zero".
Why do we have/need such an a…
 updated 9 months ago
 17 replies
 2 Medals
Mathematics

RolyPoly:
Group Title
Suppose \(E\subset R\), \(z\in R\) and \(x\le z \forall x\in E\). The upper bound \(z_0\) of the set E is called the least upper bound of E…
 updated 9 months ago
 15 replies
 2 Medals
Mathematics

RolyPoly:
Group Title
Let \(x:(0, \pi) \rightarrow \mathbf{R} ^2\) be the path given by \(x(t) = (\sin t, \cos t + \ln ( \tan\frac{t}{2} ) )\), where t is the ang…
 updated 9 months ago
 1 reply
 No Medals Yet
Mathematics

RolyPoly:
Group Title
Suppose G is a simple undirected planar graph.
Prove that G contains a vertex with degree at most 5.
 updated 9 months ago
 20 replies
 2 Medals
Mathematics

RolyPoly:
Group Title
<Graph theory>
Suppose G=(V,E) is a simple undirected graph with no selfloop; moreover, the graph G has n=V \(\ge\) 1 vertices, m=E edg…
 updated 9 months ago
 33 replies
 No Medals Yet
Mathematics

RolyPoly:
Group Title
Suppose there are m different hunters and n different rabbits. Each hunter selects a rabbit uniformly at random independently as a target. S…
 updated 9 months ago
 33 replies
 1 Medal
Mathematics

RolyPoly:
Group Title
Consider integer solutions to the equation:
\(x_1+x_2+x_3+x_4+x_5=10\)
How many nonnegative integer solutions are there such that \(x_1>x_2…
 updated 9 months ago
 22 replies
 3 Medals
Mathematics

RolyPoly:
Group Title
Consider integer solutions to the equation:
\[x_1+x_2+x_3+x_4+x_5=10\]
How many nonnegative integer solutions are there such that \(x_1 = x…
 updated 9 months ago
 12 replies
 2 Medals
Mathematics

RolyPoly:
Group Title
<Recursion>
Consider f(0) = 0 and for n \(\ge\) 1, f(n) = f(⌊n/2⌋) + 1. Find a recursion formula for the function.
 updated 9 months ago
 37 replies
 2 Medals
Mathematics

RolyPoly:
Group Title
Compute
\[\log_2(\sum_{k=0}^{1024} C(1024,k) *k)\]
 updated 9 months ago
 1 reply
 1 Medal
Mathematics
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