1
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0answers
25 views

Solving N for HN=0, Given H is a special type of skew symmetric (n x n, n is a odd number) matrix.

Solving $N\ \mathrm{for}\ H \times N =0$, given $H$ is a special type of skew symmetric matrix $(n \times n, n\ \mathrm{is\ an\ odd\ number}\ n=2k+1)$, 0 on diagonal and 1, -1 in off-diagonal ...
3
votes
1answer
68 views

If $I + A + \cdots + A^{n-1} = O$, $A$ a square integer matrix, $n$ odd, for what $k$ does $\det(\sum_{i = k}^{n-1} A^i) = \pm 1$?

This question is, in a sense, homework. I'm taking a problem-solving seminar which uses questions like these, the first question on the 2010 Virginia Tech Regional Math Competition, as fodder. The ...
1
vote
3answers
44 views

Consider the following system of linear equations..

Story cut short, I have an exam in a weeks time and this is a question off a previous exam paper - I'm unsure as to how I should go about it as there are 4 variables with only three linear equations.. ...
0
votes
0answers
53 views

Strategy in solving linear equations with 3 unknown variables

I have an equation with this form: $ A x + B y + C z = N$ $A$, $B$, $C$, and $N$ are known. $A$, $B$, $C$, $N$, $x$, $y$, and $z$ are positive integers $>= 0$. I need to find out values of ...
0
votes
2answers
67 views

How to solve this quadratic form equation?

Let $Q(x,y,z)=7x^2+7y^2-2z^2-10xy+8xz+8yz$ be a quadratic form and $A = \begin{bmatrix} 7 & -5 & 4 \\ -5 & 7 & 4 \\ 4 & 4 & -2 ...
1
vote
1answer
13 views

Algorithm to find out on which position ZX is?

I am having the following problem. Lets consider the alphabet. From A-Z there are 26 letters. If its for example AA, then its ...
0
votes
0answers
44 views

Prove solution does not exist for inequalities system

I have an inequalities sytem like the following: Example > x+y+z <= A > x+y <= B > x+z > C > y+z > D > x >= E Let A,B,C,D,E be any ...
1
vote
1answer
59 views

How to calculate per unit costs for multiple items

I had a supplier give me a quote last week that seems very strange, can someone help me out? The quote is for IT hardware, but for simplicity (and anonymity) I'll use apples and oranges: ...
1
vote
2answers
49 views

Real Life Rounding Phenomena When Solving for Variables

I have a question that I've been thinking a long time about without being able to come up with an answer and would appreciate some help: I am attempting to subtract two distinct fees from a total ...
0
votes
2answers
117 views

Linear Algebra and a cube

I am currently working no a linear algebra question and do not understand how to solve it. The questions gives: ...
0
votes
1answer
98 views

Solving a tough system of linear equations

I have three equations and have to solve for $x, y, z$. $$ l_1l_2 + m_1m_2 + n_1n_2 = 0 $$ $$ xl_1 + ym_1 + zn_1 = 0 $$ $$ xl_2 + ym_2 + zn_2 = 0 $$ After eliminating a variable (from the last two), ...
0
votes
1answer
63 views

Stuck solving an equation using the floor operator.

I am not entirely familiar with the equation ninja'ing involving the floor operators. Here is my problem. I need to solve for $x$. Everything is an integer, including $x$: $$ a - 1 = \lfloor {\frac{x ...
3
votes
1answer
102 views

Proving there are infinitely many integers having the identical set of prime factors.

Let positive integers $a$ and $b$, and let $a_0, a_1, a_2 \ldots$ where $a_i = a + b*i$ is the infinite arithmetic sequence they determine. Prove that there are infinitely many $a_i$ having the ...
0
votes
1answer
55 views

Norm, limit, and max norm

For any $\vec{u} \in \mathbb{R}^2$ prove that $$\lim_{p\to \infty} \|\vec{u}\|_p = \max (|u_1|, |u_2|)$$ Then, when $p\to\infty$ we get $||\vec{u}||_{\infty}$. And we get the max norm, ...
1
vote
1answer
85 views

Question about the matrix representation of the differentiation map on the subspace generated by $\{1, t, e^{t}, e^{2t}\}$

As mentioned in a previous post (I think), I've been trying to learn some linear algebra, and so I've begun to post little questions whose answers I'm sure are obvious to most here; this is just a way ...
1
vote
1answer
131 views

A proof about affine subsets

Let $V$ be a vector space and $S$ a nonempty subset of $V$. I want to show that $S$ is an affine subset (a translated subspace of the form $\{v\} +$ $U$, for $U$ a subspace of a vector space $V$ and ...
0
votes
1answer
27 views

Equation matching after inserting a value.

A little confusion I have got, In this question (in the middle), $$\chi''(r) + \frac{d - 1 + 2\beta}{r}\chi'(r) + \left(k^2 + \frac{\beta(\beta + d - 2)}{r^2}\right)\chi(r) = 0.$$ Form this line he ...
4
votes
1answer
110 views

Is there a better way to solve this problem in Linear Algebra?

Well I have the following problem: Let $\alpha = \{v_1,v_2,v_3\}$ and $\beta=\{u_1,u_2,u_3\}$ be two bases of $\mathbb{R}^3$ such that $v_1=(1,0,1)$, $v_2=(1,1,0)$ and $v_3=(0,1,1)$. It's known that ...
2
votes
1answer
56 views

Linear Algebra; computational problems

I dug this problem up from an old exam. I am not asking how to solve them, but I want to get a "feel" for the problem. I could technically solve this brutally,I just want to develop some problem ...
1
vote
1answer
124 views

find the value of 1/(2+1/(4+1/(4+1/(…))))

the question is to find the value of this ugly non-stopping fraction $$\frac{1}{2+\frac{1}{4+\frac{1}{4+\frac{1}{\ldots}}}}$$. I have totally no clue; thanks for the help! How am I suppose to solve ...
3
votes
2answers
138 views

Evaluating decay rate with trigonometric explanation

According to the equation 4, $$\phi(0,t)= \frac{A_0}{(1+\frac{2t^2}{R^4})^{3/4}}\cos \left(\sqrt2 t+ \frac{3}{2}\tan^{-1}\left[\frac{\sqrt2 t}{R^2}\right]\right)\tag{1}$$ what conditions makes, ...
2
votes
1answer
194 views

Searching for the value of $p_5$

Reference post: click here Given, \begin{eqnarray} &&\Delta p_5-p_5+3S^2p_5 +\frac{SZ}{576\sqrt{\lambda}}(3Z-5S^3) \left(\frac{15g_5}{\lambda^2}+1\right)^2\nonumber\\ ...
3
votes
1answer
323 views

Evaluating the time average over energy

For more info see the article equations 37 Edit: The $\varepsilon ^3 $ has vanished due to time average. But how to get the 4th order? Let us define some function for scalar field $$\phi= ...
0
votes
1answer
42 views

Frequency determination from Dimension analysis

the time averaged total energy, $\bar E$, has the following $\varepsilon$ expansion in $D$ dimension: \begin{equation} \bar{E}=\varepsilon^{2-D}\frac{E_0}{2\lambda}+ \varepsilon^{4-D}E_1 ...
2
votes
2answers
92 views

Simultaneously solving of equations

I am trying to refresh some math skills and I am struggling over the following problem. I tried to solve it with the help of a number of sources (i.e. http://www.idomaths.com/simeq.php), but I haven't ...
8
votes
2answers
328 views

Solving matrix equations of the form $X = AXA^T + C$

I'm trying to solve this matrix equation: $$X = AXA^T + C$$ In particular, $$ X = \begin{bmatrix} 1.5 & 1 \\ -0.7 & 0 \end{bmatrix} X \begin{bmatrix} 1.5 & -0.7 \\ 1 & 0 ...
2
votes
3answers
976 views

Linear independence and dependence of vectors

I am really stuck in this problem, I have only 2 days to learn matrix's base, and its generator. My problem is that I know definitions but I don't understand intuitively what they mean. What I know: ...
1
vote
1answer
98 views

uncertainty in solving constraint problem

There is a class of problems that I need to investigate the constraints of the variables in the problem and build a linear system to solve it. I find that I have no "feeling" about whether the ...
0
votes
1answer
901 views

Can this crate have even numbers in all rows and columns?

A milk crate holds 24 bottles in four rows and six columns. Can you put 18 bottles of milk in the crate so that each row and each column of the crate have an even number of bottles in it?
2
votes
2answers
69 views

Proving two expressions can never be simultaneously satisfied

I have a very simple problem, the technique of which I want to apply to more difficult problems. Here is the simple example version: Suppose we have four functions: $f_1(x)=\sin(x)$, $g_1(x)=0$, and ...
1
vote
2answers
376 views

Multiplying Reciprocal Exponents

This is the problem I have: $$y^{\frac{3}{2}} = 5y$$ What I tried so far was raising $y^{\frac{3}{2}}$ to the $\frac{3}{2}$, making it equal $1$, but I had trouble raising $5y$ to that power.
2
votes
2answers
1k views

An exercise from a linear algebra book (hoffman and kunze)

I am not sure how to solve this exercise: Find all solutions of $$\begin{align*}2x_1-3x_2-7x_3+5x_4+2x_5&=-2\\ x_1-2x_2-4x_3+3x_4+x_5&=-2\\ 2x_1\qquad-4x_3+2x_4+x_5&=3\\ ...
5
votes
2answers
785 views

Invertible Matrices are dense

While reading about linear algebra for math olympiads in these notes, I came across the following assertion: Remark. The set of invertible matrices form a Zariski (dense) open subset, and hence to ...
1
vote
0answers
151 views

Pair of equations with any equal number of variables with unique solution?

$(a+b+c\cdots)\neq(a^{2}+b^{2}+c^{2}\cdots)$ given all distinct values for the variables? When I came across this topic, it made me curious as to explore other possibilities, as here, what other two ...
0
votes
0answers
60 views

Help solving for $x$, $y = c_1 + 640a + 16x$ OR $y = c_2 + 648b + 16x$ with consistent result.

I'm writing a program. Part of the program fetches a cryptic memory value from another program (which stores information on a value i'm looking for) and reverse engineers it. I need help figuring out ...
1
vote
2answers
379 views

Reverse Cuthill McKee Ordering and Solution of systems of Linear Equations

I just learned about the RCM. I am trying to solve a problem that is a result of fluid dynamics and chemistry so I have a very large sparse matrix. I also learned reducing the bandwidth would ...
3
votes
1answer
147 views

Linear Algebra problem: intersection of a subspace with a cone.

In $\mathbb{R}^n$, consider the closed cone $$C^+ = \{ (x_1, \ldots, x_n) : x_i \geq 0,~~i= 1, \ldots, n\}.$$ Let $S \subseteq \mathbb{R}^n$ be a subspace (of any dimension) such that $S \cap C^+ = ...
3
votes
4answers
746 views

Solving For A Linear Operator

I'm currently learning about linear operators, and the chapter in my book describing them only has examples with predefined linear operators. One of the first questions asks: ...