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Jan
21
comment Homogeneous system of linear equations over $\mathbb{C}$
Your intuition is right. Take, for example, $x_2=17$, $x_4=42$, and you can solve A for $x_1$ and $x_3$. I don't know enough about Mathematica to tell you what's gone wrong.
Jan
21
answered Homogeneous system of linear equations over $\mathbb{C}$
Jan
21
comment Homogeneous system of linear equations over $\mathbb{C}$
By the way, you must be mis-using Mathematica, as a homogeneous linear system with more unknowns than equations is guaranteed to have non-trivial solutions.
Jan
21
comment Homogeneous system of linear equations over $\mathbb{C}$
Does this mean you haven't done row reduction of matrices yet?
Jan
21
comment Why is the set of integers modulo 3 a field? Also why is integers modulo prime a field?
The set of integers isn't a field. But integers mod 3 isn't integers. Do you know how arithmetic works mod 3?
Jan
21
comment Why is this incorrect (regarding differentiating the natural log)?
It's logarithm of $3x^2+3$, not logarithm times $3x^2+3$.
Jan
21
comment Linear Algebra: equivalence classes
Using just row operations, you can bring any matrix to reduced row-echelon form. There are only a few reduced row-echelon forms for $3\times2$ matrices over the field of $5$ elements. Then you can use column operations on those forms to get down to a complete set of row-column inequivalent matrices.
Jan
21
comment how to find number of maximum
As you are a student, do you prefer to work things out on your own, or do you prefer for someone else to do all your work for you? I'm guessing you prefer the satisfaction of working things out on your own. If so, then consider that A.D may also be a student, and may wish the joy of working things out, instead of seeing it all done by someone else.
Jan
21
comment Property similar to decreasingness
Isn't it decreasing if $N=1$? You have $k\gt j$ implies $a_k\lt a_j$.
Jan
21
revised Hypothesis testing, find out critical value $c$
couple of typos
Jan
21
comment Generating set of a submodule
If $2x+3y-5z=0$, then $5$ divides $2x+3y$, so $5$ divides $2x-2y$, so $5$ divides $x-y$.
Jan
21
comment Generating set of a submodule
Perhaps instead of subspace you want subgroup or submodule?
Jan
21
comment graph theory: upper bound on edge number, given number of vertices and
I think the answer, absent further restrictions on the graph, is the greatest integer not exceeding $n\Delta/2$.
Jan
21
answered Lagrange's Theorem on sum of four squares.
Jan
21
comment Families of sets, determination of SDR (system of distinct representatives)
The obvious necessary condition is also sufficient, by Hall's Marriage Theorem. There are constructive proofs of Hall's Theorem --- proofs that you can apply to given problems to find SDRs --- but for small examples as here, educated trial and error is probably the way to go.
Jan
21
comment Prime decomposition of an integer: methods of determining the prime factors $ p_1, p_2, …, p_r$ and powers $k_1,k_2, …, k_r$
Books have been written on methods for factoring integers. Some of the methods depend on very advanced mathematics. Here are a few keyphrases you could search for: Pollard rho; Pollard $p-1$; quadratic sieve; elliptic curve factorization method; SQUFOF; number field sieve.
Jan
21
comment how to find number of maximum
I see no evidence that OP has a solution to check.
Jan
21
comment how to find number of maximum
Not leaving much work for OP to do.
Jan
21
comment What are the features of $n/d, n \rightarrow d, d \rightarrow \infty; n, d \in \mathbb{N} $?
Ross, the rationals are dense in the reals. Every non-empty open subset of $[0,1]$ contains infinitely many numbers $n/d$ with $n,d$ positive integers and $n\lt d$.
Jan
21
comment Elliptical Integrals and graphing plot
Is this a math question, or a programming question? If it';s the latter, it may be more suitable for the programming site.