# linear

1. ### Linear dependence question

Let f_1(x) = \sin x,~ f_2(x) = \cos(x + \frac{\pi}{6}), and~ f_3(x) = \sin(x - \frac{\pi}{4}) for 0 <= x <= 2\pi. Show that { f_1, f_2, f_3 } is linearly dependent by finding constants c and k such that cf_1 - 2f_2 - kf_3 = 0 . what is c and k?
2. ### Linear dependency and independence

Can this be explained by use of one solution, no solution or infinitely many solutions? If not, just summarize it for me the way you understand it. Sent from my SM-G955W using Tapatalk
3. ### error: linear inequality (absolute function)

hello, I tried to solve the following inequality: abs(-2x+1)>2/3x+1 but get wrong results: -2x+1>-2/3x-1 I add 1 then +2x then multiply with 3 and divide by 4 I get: x<3/2 and -2x+1>2/3x+1 cancel out 1 then +2x 0>8/3x so I get x<0 surely this inequality is true for some x>0 - do...
4. ### linear or non-linear

May I know the reason why the differential equation: |dy/dx| = y is non-linear differential equation?
5. ### Elementary Linear Algebra 2nd Edition.

Hi! Please find this interesting Algebra book in the following link: https://smartmanmaths.com/2017/10/26/elementary-linear-algebra-2nd-edition/ What do you think about it?
6. ### Problems about linear combination, direction numbers, and transposes

Hello everyone, I have some math homework here I can't quite understand: Q3: (a) Express the given vector as a linear combination of base vectors: (b) Find the direction numbers and direction cosines of each vector. c) Find the transpose of each vector. i) v = [2]...
7. ### Linear Programming Problem!

The semester has just started and you want to come up with an optimal daily schedule for your off-class time, i.e. you want to know the time you need to allocate to studying, and the time you need to allocate for extra- curricular activities. For a more balanced life, you want to ensure that the...
8. ### Converting formula to linear relationship

I am struggling with converting formulae to the linear form Y = mX +C For example if I have the relationship ay=b^x and I need to express this in linear form using logs, I get: logy+ loga = xlogb not sure how to get this to the form Y=mX+C because if I move the loga onto the other side I...
9. ### FLT from a system of infinite linear equations

FLT from a system of infinite linear equations As told from the Power properties they can be written as Sum: $$A^n= \sum_{x=1}^{A} M_n$$ $$B^n= \sum_{x=1}^{B} M_n$$ $$C^n= \sum_{x=1}^{C} M_n$$ Where: $$M_n=[x^n-(x-1)^n]$$ Than FLT state: $$C^n=A^n+B^n$$ Can be rewritten...
10. ### Generating a linear system for popularity calculation

This is a half mathematical half computer science question. I am working on matlab on a mathematical problem. I want to generate a linear system for the calculation of popularity of people (a vector x) in a generic social network, given a simple matrix of friendship F. If user 1 and user 2 are...
11. ### Should span be a finite linear combination only?

Wiki says infinite linear combination should be excluded off of the definition of span. So should we answer "Yes" to the following question appearing in UC Davis notes?:
12. ### What is line vector?

I am reading a book on vector analysis, but the statement defining "line vector" confuses me because I can't catch the author's English, especially "forms a part". Following is a screenshot of this definition of line vector in the text, highlighted by a red line. Could you please tell me what a...
13. ### Linear Differential equation with constant coefficient

A solution of $(D^2+1)^3y=\sin x$ is A) \sum_{n=1}^{3} (c_nx^{n-1}\sin x+d_nx^{n-1}\cos x) for some c_n, d_n \in R, 1 \leq n \leq 3. B) \sum_{n=1}^{3} (c_n \sin^n x+d_n \cos^n x) for some c_n, d_n \in R, 1 \leq n \leq 3. C) \sum_{n=1}^{3} (c_n \sin n x+d_n \cos n x) for some c_n, d_n \in R, 1...
14. ### Solve the Linear Equations

I tried to solve the equations in different ways but unsuccessful. Kindly someone solve this : If $a, b, c$ and $d$ satisfy the equations $a + 7b + 3c + 5d = 16$ $8a + 4b + 6c + 2d = âˆ’16$ $2a + 6b + 4c + 8d = 16$ $5a + 3b + 7c + d = âˆ’16$ Then $(a + d)(b + c)$ equals to ...
15. ### Can't solve this First Order Linear Differential Equation

Gaah, it's 4am my brains slow. I know how to solve this, please delete this thread. Sorry and thanks.
16. ### linear congruence

Find the set of solutions of each of the linear congruence: a) x â‰¡ 3 (mod 5). b) 2x â‰¡ 5 (mod 9).
17. ### Non-linear Equations

Show that the (non-linear) equation system: $x^{2}$ + $y^{2}$ -$u^{2}$ - v=0 $x^{2}$ + $2y^{2}$ -$3u^{2}$ - $4v^{2}$=1 can be solved in (u, v) in a neighbourhood of (1/2,0,1/2,0) How to show this and also calculate the derivative of u and v wrt (x,y)?
18. ### How to linearize function?

Hello everyone, To be able to use following objective function in CPLEX, we must first linearize the function, because CPLEX cannot solve function that are non-linear in the decision variables. xj; yij and yjk are decision variables. Who can help? Taking the square root is not good, since this...
19. ### Linear ordinary differential equation

Here is an equation Vsinwt=iR+Ldi/dt i have to solve this equation with linear method ,i.e i'+p(t)i=Q(t) i have solved it to the step Li'e^rt+iRe^rt=e^rtVsinwt by initial steps and by finding integrating factor ,but now i stuck ,just don't know that what to do with that L with first most...
20. ### System of linear congruences: 2xâ‰¡3(mod 5), 61xâ‰¡15(mod 6), 8xâ‰¡16(mod 56)

Hi, I have this exercise about a system of linear congruences. Solve it, if possible and get all the solutions: $\begin{cases} 2x \equiv 3 \mbox{ (mod 5)} \\ 61x \equiv 15 \mbox{ (mod 6)} \\ 8x \equiv 16 \mbox{ (mod 56)} \end{cases}$ I have tried to resolved, can you tell me if is...