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Feb
12
comment Equations With Two Linear Congruences
It seems to me that if $x$ is an integer then the right side's a multiple of $7$ but the left side isn't, so there can't be a solution. Are you prepared to accept fractional values of $x$?
Feb
12
revised discrete logistic dynamics problem
edited tags
Feb
12
comment discrete logistic dynamics problem
You may find the identities $\sin^2u+\cos^2u=1$ and $\sin2u=2\sin u\cos u$ come in handy.
Feb
12
comment discrete logistic dynamics problem
$n$ is a variable, not a constant. You meant $b$?
Feb
12
comment Condition for mapping linearly independent vectors to linearly independent vectors
If $\dim W\lt\dim V\lt\infty$ then you can't have a trivial kernel. Also, there's nothing in the original problem about a basis.
Feb
12
comment Finding the $g'$ of 2 functions
The first line of (a), that $xg^2$ should be $g^2$.
Feb
12
comment Condition for mapping linearly independent vectors to linearly independent vectors
Not true if the dimension of $W$ exceeds that of $V$. Also not true in infinite dimensions.
Feb
12
comment Nullspace of matrix with multivariate polynomial entries
@YACP, yes, posted 16 Oct, closed 17 Oct, deleted 19 Oct. On MO, people are expected to clean up their own questions, which OP made no effort to do. The customs at m.se are different.
Feb
12
comment When is a linear recurrence relation solvable?
Yes.${}{}{}{}{}$
Feb
12
comment Randomly Assigning a Bill
In principle (although with probability zero) you could wind up tossing the coin forever. So long as you reproduce the binary expansion of, say, $1/5$, you don't know whether $x$ will turn out to be bigger than $1/5$, or smaller.
Feb
12
revised Prove Using Complex Multiplication
edited tags
Feb
12
comment Prove Using Complex Multiplication
Do you know an identity for $\tan(x+y)$? and do you see how it might come in handy?
Feb
12
comment Condition for mapping linearly independent vectors to linearly independent vectors
All four answers are wrong. The second set is linearly independent if $f$ is one-one, but it's not an "only if". Try to find an example of a linear map that isn't one-one but still preserves linear independence of some (not every!) set.
Feb
12
revised Another trigonometric equation
typos in title
Feb
12
comment Another trigonometric equation
Where are you getting these? Why are they of interest to you?
Feb
12
revised Some trigonometric equation problems
edited tags
Feb
12
comment Some trigonometric equation problems
This is probably the hard way, but it ought to work. Multiply through by $64$, write $2+2\cos(2k\pi/13)=2+\zeta^k+\zeta^{13-k}$ where $\zeta=e^{2\pi i/13}$, multiply everything out, use $1+\zeta+\cdots+\zeta^{12}=0$ and standard formulas for the Gauss sum $\sum\zeta^{k^2}$. Similarly for the second one, but with $11$ instead of $13$.
Feb
12
comment A singular matrix limit
@Kaster, that's what's wanted, no? The question asks, what if $B$ is singular?
Feb
12
comment Like Diophantine equation
For $x=2$, you get a positive $y$ for every positive $n$ --- just look at the formula! For $x=2$, I you can certainly get $y$ to be an integer, but I don't think you can get $n$ and $y$ both integers. I don't know how to show you the graph --- I recommend you find some graphing software, and let it do the work.
Feb
12
answered Rubik Cube finite non-abelian group