# linear

1. ### Linear Approximation to Estimate a number

I have a couple of online hw questions that have got me stumped. The first states: "Use a linear approximation to estimate the following number" and then provides the number (2.9)^4. the practice problems from the textbook indicate that the answer is simply 2.9^4 which would be 70.7281. This...
2. ### Linear (in)dependence

Hi guys, I'm stuck with a problem which is, I believe, simple, but I can't solve it by myself. So, I have 4 vectors a,b,c,d that are linearly independent. I am supposed to check whether the following vectors are dependent or independent: a1 = a+2c+d b1 = 2a-b+c c1 = a+c+d Thank you in advance. :D
3. ### Span and linear dependence

Dear everyone, l really get confused when reading some textbooks on linear algebra : Suppose there are two vectors in R3, u= (3,1,0) and v = (1,6,0). Firstly, u and v are linearly independent because neither vector is a multiple of the other. IF w is a linear combination of u and v...
4. ### Linear Programming App

Hi, New app named "Linear program solver" designed for students who want to solve any linear problem. this app include all methods you need like graphical method, algebraic method, table method and matrix method. https://play.google.com/store/apps/details?id=com.aoujapps.linearprogramsolver
5. ### Confusion about span in Linear Algebra

Hi there, this is my first post here. I am currently studying some control theory related stuff and it's basically linear algebra. However, I have some problems. I have given this exercise on which I already got an answer in Mathematics Stackoverflow: However, when checking other sources I...
6. ### Solve the Linear ODE of first order first degree

Hi all, I'm stuck with this problem. Please help me to identify which method to use. Attaching the question. Thanks a lot for your help.
7. ### Linear combination of random variables, convergence for a large number of variables

Hi, I have positive random variables X1, X2, X3, ..., Xn such that their sum=1 (so they are random, subject to constraints that each Xi is positive their sum has to be 1.. so all are fractions). Now, I have a function f=C1.X1+C2.X2+C3.X3.....+Cn.Xn where C1, C2, ....Cn are known...
8. ### Linear independence of functions

Whether Cos 3x and Cos (3x + Pi/2)are linearly independent or not in the interval (-infinity, infinity)? My attempt: I calculated the Wronskian that comes out to be -3 (independent of x) that signifies that this function is linearly independent because the sufficient condition for the set...
9. ### quadratic program to linear program

Hi Community, I am new in this forum and I hope that I can help you as well as you can help me to solve my problems. :) I have a quadratic program, where I want to minimize: \sum_{i=1}^n \sum_{j=1}^n x_i x_j a_{i,j} and every x_i \in \{0,1\}So all in all it is a quadratic problem of the...
10. ### Find duplicate Geometry with Linear Transform

Hey, I'm working on an algorithm that finds duplicate Geometry. Here's what I do: I'll take a mesh, get all it's vertices and find the average of them: x = average(a, b, c, d, e, f) then I'll get the distances of the average to the vertices: ad = dist(x, a) bd = dist(x, b) cd =...
11. ### Linear span

Can someone clarify what it means when a spanning set of vectors spans the smallest subspace. Presumably, if the set of vectors are dependent I can find a basis set whose linear combinations will span the smallest subspace determined by the dimension. But Wiki mentions the intersection of...
12. ### Solve for x in T(x) = Ax in linear transformation

When solving for x as given in question (photo attached), I can't seem to get the right x. I solve for x using row reduction with augumented matrix 1 -4 4 |-4 0 1 -4 |-1 2 -9 8 |-3 and I get x = (4,3,1) which is wrong, with the error message that I'm solving wrongly. Using graphic...
13. ### Linear approximation

Using linear approximation calculate sqrt(99)?
14. ### Feedback for an answer involving Span, Dimension and Linear Independence

Hi guys, I have worked out an answer to the following question, but it's stretching my understanding of Linear Algebra to the limit, soâ€¦ if anybody could have a look at it, and just tell me whether my reasoning is sound, it would be a great help... Let v_1,â€¦,v_k,u,w be vectors in the...
15. ### Check, for constructing nice set of linear equations

Hi Well, I was struggling with solving these linear equations for days. more accurately, It solved but the answers do not check with what I have, so want to find where I have mistaken. It would be appreciated if you can check with me that my understanding is correct for the problem. (do not...
16. ### Linear equation with Kronecker delta, Plz help

if (f,g) are variables, The constants are: A,B,C,D, (vary with i,&j) S1,S2 (not depended on i&j) . Sij = Kroencker delta (=1, when i=j, & =0:if iâ‰ j ) Aij*fj + Bij*gj =S1. S0j Cij*fj + Dij*gj =S2. S0j i,j=0,1,2,3.............N Is it correct what I am getting [that the values of...
17. ### Linear algebra, sum of subspaces

Let U1, U2, U3 be subspaces of R^4: U1 = {(a,b,c,d):a=b=c} U2 = {(a,b,c,d):a+b-c+d=0; c-2d=0} U3={(a,b,c,d):3a+d=0} show that: a) U1 + U2 = R^4; b) U2 + U3 = R^4; c) U1 + U3 = R^4; whish of the sums are direct sum?
18. ### Convergence in a normed vector space - Linear operator

Having X a normed vector space. If f is a linear operator from X to â„ and is not continuous in 0 (element of X) , how can we show that there exists a sequence xn that converges to 0 for which we have f(xn) = 1 (for all n element of â„•). Any help would be greatly appreciated, thank you.
19. ### System of linear equations

see the attached, please https://ufile.io/rup5u no of the equations is 198 no of variables in each equation is 116 all the equations are linear what method could be used to solve such equations [indeterminate equations] Thanks
20. ### # of linear equations <> # of variables

How to solve the following equation: (I) is imaginary unit A+I*B= [(C*X1+D*Y1+ E*X2+F*Y2)]+ I*[ (G*X1+H*Y1+ M*X2+J*Y2)] ---- This equation should satisfy several boundary conditions. at each point of these boundary the constant [A, B, C,D,E,F,G,H,M,J] are known. Number of points of...