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Questions Asked

RolyPoly:
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 days ago
 No Medals Yet
Mathematics

RolyPoly:
What can you tell about the eigenvalues of matrix \(A^2\) if an eigenvalue of matrix \(A\) is \(\lambda\) and the corresponding eigenvector…
 updated 12 days ago
 1 reply
 No Medals Yet
Mathematics

RolyPoly:
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 days ago
 33 replies
 3 Medals
Mathematics

RolyPoly:
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 13 days ago
 33 replies
 3 Medals
Mathematics

RolyPoly:
Why do we use radian instead of degree in "higher mathematics", for example, in calculus?
 updated 24 days ago
 9 replies
 No Medals Yet
Mathematics

RolyPoly:
It is known that a system has infinitely many solutions.
What happens when such a real system has a unique solution?
 updated 25 days ago
 No Medals Yet
Mathematics

RolyPoly:
Given an undirected graph H, let C be the adjacency matrix of H. What is the meaning of entries in \(C^n\)?
 updated 25 days ago
 20 replies
 1 Medal
Mathematics

RolyPoly:
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 one month ago
 13 replies
 No Medals Yet
Mathematics

RolyPoly:
Use MI to prove that \(n^21\) is divisible by 8 for any positive odd integer n.
 updated 2 months ago
 8 replies
 1 Medal
Mathematics

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

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

RolyPoly:
<Linear Algebra>
In the process of solving a system of linear equations, we have three elementary row operations, which are
(I) Exchange t…
 updated 2 months ago
 39 replies
 3 Medals
Mathematics

RolyPoly:
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 3 months ago
 82 replies
 1 Medal
Mathematics

RolyPoly:
Whether zero is a natural number or not is still controversial.
What is the (mathematical) argument for 0 *NOT* being a natural number?
 updated 3 months ago
 8 replies
 1 Medal
Mathematics

RolyPoly:
"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 3 months ago
 17 replies
 2 Medals
Mathematics

RolyPoly:
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 3 months ago
 15 replies
 2 Medals
Mathematics

RolyPoly:
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 3 months ago
 1 reply
 No Medals Yet
Mathematics

RolyPoly:
Suppose G is a simple undirected planar graph.
Prove that G contains a vertex with degree at most 5.
 updated 4 months ago
 20 replies
 2 Medals
Mathematics

RolyPoly:
<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 4 months ago
 33 replies
 No Medals Yet
Mathematics

RolyPoly:
Suppose there are m different hunters and n different rabbits. Each hunter selects a rabbit uniformly at random independently as a target. S…
 updated 4 months ago
 33 replies
 1 Medal
Mathematics

RolyPoly:
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 4 months ago
 22 replies
 3 Medals
Mathematics

RolyPoly:
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 4 months ago
 12 replies
 2 Medals
Mathematics

RolyPoly:
<Recursion>
Consider f(0) = 0 and for n \(\ge\) 1, f(n) = f(⌊n/2⌋) + 1. Find a recursion formula for the function.
 updated 4 months ago
 37 replies
 2 Medals
Mathematics

RolyPoly:
Compute
\[\log_2(\sum_{k=0}^{1024} C(1024,k) *k)\]
 updated 4 months ago
 1 reply
 1 Medal
Mathematics

RolyPoly:
<Soft question>
How is calculus applied in Computer Science?
 updated 4 months ago
 No Medals Yet
Mathematics

RolyPoly:
<Graph Theory>
Find the number of paths of length 5 in the complete bipartite graph \(K_{4,9}\).
 updated 4 months ago
 70 replies
 3 Medals
Mathematics

RolyPoly:
Use Green's theorem to calculate the area under one arch of the cycloid:
x = t  sint
y = 1  cost
 updated 4 months ago
 No Medals Yet
Mathematics

RolyPoly:
How to parametrize the equation y^2 = x^3?
 updated 4 months ago
 4 replies
 1 Medal
Mathematics

RolyPoly:
We have: \[\int_0^1 \int_{3y^2}^{4y^2}\int_{\sqrt{z3y^2}}^{\sqrt{z3y^2}} dxdzdy\]
Task: change the order of integral to dxdydz
 updated 5 months ago
 8 replies
 2 Medals
Mathematics

RolyPoly:
We have :
\[\int_0^1 \int_{\sqrt{44y^2}}^{\sqrt{44y^2}} \int_{x^2+3y^2}^{4y^2}dzdxdy\]
Task: change the order of integral to dxdzdy
 updated 5 months ago
 44 replies
 2 Medals
Mathematics
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