Span Definition and 209 Threads

So let's say I have a function that I want to find out if is in the span of two other functions, for example, a*f + b*g = h, where f, g, and h are functions, and a and b are constants. Let's say I find a solution where a and b are not constants. Does that still mean that h is in the span of f...

So pretty frequently I encounter questions like a) Are these vectors linearly independent? b) Do they span all of R? Why? As I understand linear dependency, the linear combination of the vectors in question exists as the Null vector for some set of coefficients.

Homework Statement Hi, I have to prove that there's no exist a generating set for "x" with less of "n" vectors when "n" is the dimension of the basis of "x" Homework Equations is there a span(x) whith dimension m? when m<n and n is the dimension of the basis The Attempt at a Solution...

What size of HSS beem do I need to cross a 40 foot span with 500 kilos even distributed still weight. it will be used to hold 1/2 of a roof. there will be no center post. no wind. structure is inside. Thanks so much. Big help I just don't know this stuff.

This might sound crazy, but I want to study pronging human life span. I am thinking of majoring molecular nanotechnology so that I can use this major to construct an artificial enzyme(medical nanorobot) that lengthens telomere (I know this is not the only issue of aging and death). I am not...

Homework Statement Say we have the plane, x+2y+4z=8 (part of a larger problem) Homework Equations The Attempt at a Solution The vectors (8,0,0) and (0,0,2) both lie in the plane. They are linearly independent. But (0,4,0) lies in the plane and is not a linear combination of the first two...

In order to increase production rate a reactor set point was increased from 160 psig to 190 psig. The reactor pressure transmitter was recalibrated from 0-200psig to 0-300 psig what is the percent span for old and new set points. Can you please explain to me how to find the answer. The book says...

Homework Statement What is the span of {(1; 1; 0),(0; 0; 2)}? The Attempt at a Solution So the span is λ1(1; 1; 0) + λ2(0; 0; 2) But how should I express my answer? The given answer on the sheet is as below: The span is {(λ,λ,β)|λ,βεR}

Homework Statement I am trying to calculate the flexural rigidity across the span of a guitar soundboard. The soundboard is comprised of a number of struts, the shape of which can be approximated to a triangular section sitting on a rectangular section. This makes for straightforward...

I need to calculate the increase in drag due to an airbrake, however the formula includes "semi span". I'm unsure if this is simply wing span/2 or is it the length of a wing in which case it would be (wing span - fuse width)/2. Any help would be good.

Homework Statement Is the following set linearly dependent or independent? And does this set span the given space? {eX, e-x}\inC∞(R) Homework Equations The Attempt at a Solution So, if it's linearly independent, then: k1ex +k2e-x = 0 where k1,k2=0 and only 0. But if you let k1=...

Hey guys I found this forum and very informative i must say. My question is i found a similar thread but i am wondering. I am building a punching bag frame for 14 punch bags between the weight of 100-120lbs. The span is 23' by 20'. The span of 23' will be broken up with a support in...

Hello Everybody, Span efficiency factor appears in the lifting-line theory of Prandtl describing Lift and vortex drag of a finite wing. According to this theory, the most efficient wing is an elliptical one and, roughly speaking, the span efficiency factor defines an efficiency of a given wing...

Hello Everybody, Span efficiency factor appears in the lifting-line theory of Prandtl describing Lift and vortex drag of a finite wing. According to this theory, the most efficient wing is an elliptical one and, roughly speaking, the span efficiency factor defines an efficiency of a given...

How do you show that a set of linear transformations from one vector space to another spans L(V,W)? This isn't a homework question, or even a question that's in the text I'm reading (Friedberg).

hi Guys, i Needed your help to prove out the following, thanks in advance; Let u1,u2,...,ut be vectors in $\Re^n$ and $k\in\Re ,k\neq0.$ Prove that $Span\{u_1,u_2,...,u_t\}=Span\{ku_1,u_2,...,u_t\}$

Suppose that some infinite set S spans V. Then this means every vector in V is expressible as some linear combination of the vectors in S. Does this combination have to be finite? It couldn't be infinite, because that necessarily invokes notions of convergence and norm which do not...

Let A and B be subsets of a vector space V. Assume that A ⊂ span(B) and that B ⊂ span(A) Prove that A = B. I don't know how to go about this question, any help would be appreciated.

Homework Statement Give S = {(x,|x|,2|x|) | x \in R} \bigcup {(0,2,4),(-1,3,6)}, find span(S) Homework Equations I know that span of a finite set of vectors is given by <a(0,2,4) + b(-1,3,6)+c(x,|x|,2|x|)>, where a,b,c are any real numbers. Can i use that same way to find the span of this...

Hey guys, I'm just pondering a beam problem fir a structure that I'm analysing. It appears statically indeterminate to me? The beam is bolted to a support at locations A,B & C. There are two point loads between span B-C. There are no symmetrical distances or support locations etc. Initially...

Let's say I have some finite subset of vectors in, let's say, ℝ^{5} . If my set has five linearly independent vectors, they necessarily form a basis for ℝ^{5} . If I have more than 5 vectors, they are linearly dependent. If I have less than 5 vectors, they span only a subspace of ℝ^{5} not...

Suppose you have two sets S_{1} and S_{2}. Suppose you also know that every vector in S_{1} is expressible as a linear combination of the vectors in S_{2}. Then can you conclude that the two sets span the same space? If not, what if you further knew that every vector in S_{2} is expressible...

Octagonal Cross Section with Parabolically Increasing "Span" Hi all, could some one tell me what I am doing wrong in my analysis in the attached file? Its a parabolical flare column with an octagonal cross section. The effect of the parabolic flare simply stretches the octagon so that the...

I have an external HDD with a lot of information stored in it, my question is what exactly the life span of an external HDD? Thnaks in advance.

Homework Statement S_1 and S_2 are subsets of a vector space. When is this: span(S_1 \cap S_2) = span(S_1) \cap span(S_2) true? Prove it.Homework Equations The Attempt at a Solution conjecture: iff the two subsets are vector spaces.

Homework Statement My linear algebra is rusty. So to go from a reduced QR factorization to a complete QR factorization (ie the factorization of an over determined matrix) one has to add m-n additional orthogonal vectors to Q. I am unsure on how to find these. If it is extending a 3x2 to a 3x3...

Hey there, Does the set (z^n ; n\in N) span L^2[0,1]? Thanks in advance

Homework Statement Hi all, I am struggling with getting an intuitive understanding of linear normed spaces, particularly of the infinite variety. In turn, I then am having trouble with compactness. To try and get specific I have two questions. Question 1 In a linear normed vector space, is...

Here is the question: Here is a link to the question: Find the value of "a" for which? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

What does it mean geometrically to say that V lies in span S, in other words that V is in a linear combination of S?

I was curious, why is it that dogs will live somewhere in the 10-20 year range, but humans make it to 80, and animals vary so much?

Homework Statement I have this span, spanned by these three vectors in R^5: \underline{a_1}= \left( \begin{array}{c} 2 \\ 3 \\ 1 \\ 4 \\ 0 \end{array} \right) \underline{a_2}= \left( \begin{array}{c} 1 \\ -1 \\ 2 \\ 4 \\ 3 \end{array} \right) \underline{a_3}=...

I am reading my linear algebra book, and in the chapter on Spanning, I got the impression that for a set to span R^n, it must contain at least n vectors. I confirmed that by searching through the forums. However, I've reached the chapter on Linear Independence and in one of the examples it...

Homework Statement Let M be the 12 x 7 coefficient matrix of a homogeneous linear system, and suppose that this system has the unique solution 0 = (0, ..., 0) \in ℝ7. 1. What is the rank of M. 2. Do the columns of M, considered as vectors in ℝ12, span ℝ12. Homework Equations The...

Why is it not possible for the columns of a matrix to span R^2 even if those columns do not span R^3?

I'm having some trouble internalizing the concept of span. The question: If u = [1,2,1]; v = [-2,2,4]; and w = [-1,4,5], describe Span{u,v,w}. The attempt at a solution: I formed a matrix using column vectors u, v, and w and row-reduced to RREF: \begin{bmatrix} 1 & -2 & -1 \\ 2 & 2 & 4 \\...

Homework Statement The problems states "All polynomials of the form p(t)= at^2, where a is in R." I'm supposed to see if it is a subspace of Pn. I've already done that but the book's answer is that it spans Pn by Theorem 1, because the set is span{t^2} Homework Equations Theorem states "1 If...

Homework Statement Determine if the following sets of vectors span the indicated space a) {[0 -6 -6], [8 -3 5], [-9 7 -2]}, ℝ3. b) {[2 1 7 -2], [3 5 4 5], [4 -4 -3 -3], [-5 0 6 -4]}, ℝ4. Homework Equations The Attempt at a Solution a) a[0 -6 -6] + b[8 -3 5]...

Homework Statement So basically, I'm studying the proof for this: "In a finite dimensional vector space, the length of every linearly independent list of vectors is less than or equal to the length of every spanning list of vectors." What the book (Axler's Linear Algebra Done Right 2e) does...

I'm designing a patio which is connected to a house on one side, 8m x 2.4m 150 x 50 x 3mm steel tubing around the outside with 140 x 50 hardwood purlins, spaced at 1m intervals (2.4m long each). I would like to span the 8m with only posts on the ends. Is this possible or will there be to...

Homework Statement Can these sets be expressed as a linear span? Justify your answers. (i) A = \{ (x,2x + y,3y,y - 2)|x,y,z \in ℝ\} (ii) B = \{ (x,y,z)|y = {z^2}\} (iii) C = \{ (a,b,c,d)|a \ne b and c \ne d\} Homework Equations The Attempt at a Solution Actually I have no problem writing down...

Homework Statement Suppose v_1,v_2,v_3,...v_n are vectors such that v_1 does not equal the zero vector and v_2 not in span{v_1}, v_3 not in span{v_1,v_2}, v_n not in span{v_1,v_2,...v_(n-1)} show that v_1,v_2,v_3,...,V_n are linearly independent. Homework Equations linear independence...

The problem is attached. I don't know why he called all 4 vectors V1, I guess it was a typo. Anyways, part I) This is not linearly independent as the determinant of the matrix containing those 4 vectors is 0 I am having trouble with part II) I think I know the answer, but I don't...

Homework Statement Consider the vector space F(R) = {f | f : R → R}, with the standard operations. Recall that the zero of F(R) is the function that has the value 0 for all x ∈ R: Let U = {f ∈ F(R) | f(1) = f(−1)} be the subspace of functions which have the same value at x = −1 and x = 1...

Homework Statement Consider the vector space F(R) = {f | f : R → R}, with the standard operations. Recall that the zero of F(R) is the function that has the value 0 for all x ∈ R: Let U = {f ∈ F(R) | f(1) = f(−1)} be the subspace of functions which have the same value at x = −1 and x = 1...

1. Can a set of 5 vectors in R6 span all of R6?I want to say that it does span, because i remember my teacher saying "don't think of the physical world," but I'm not entirely sure if it does.

Homework Statement is vector b in the span of vectors v1,v2? Give reasons. Homework Equations The Attempt at a Solution v1=(1,4,0,-1) v2=(2,7,-2,-3) b= (-1,-1,7,4) set up in matrix (v1,v2| b) and after row reduction I have (1,0,0,0),(2,-1,0,0)|(-1,3,6,6)...

Homework Statement Determine if the vectors v1=(3,1,4), v2=(2,-3,5), v3=(5,-2,9), v4=(1,4,-1) span ℝ3 Homework Equations The Attempt at a Solution So I first arranged it as a matrix, \begin{bmatrix} \begin{array}{cccc|c} 3&2&5&1&b_1\\ 1&-3&-2&4&b_2\\...

Are there any structural engineers here or know the stuff. I'd like to know this. Can structural engineers design long span beam for example 12 meters reinforced concrete beam that is as good as standard 6 meter beam in seismic performance or are 6 meter beams always better compared to 12...

Would I be correct in saying that: If Span(S)≠0 then S is linearly independant. If Span(S)=0 then S is linearly dependant. With S being a subset of V.