Span Definition and 209 Threads

Homework Statement Here's a statement, and I am supposed to show that it holds. If x,y, and z are vectors such that x+y+z=0, then x and y span the same subspace as y and z. Homework Equations N/A The Attempt at a Solution If x+y+z=0 it means that the set {x,y,z} of vectors...

Question given. Predict how the average life span of a nerve cell located in the brain differs from the average life span of a red blood cell. Provide a basis based on cellular features. I know that the average life span of a nerve cell is the life span of the organism which it lives in. The...

Linear Algebra -- Span of vectors Homework Statement Let x, y, z be non-zero vectors and suppose w=15x−10y−3z. z=3x−2y, then w=? Using the calculation above, mark the statements below that are true. A. Span(w,x) = Span(w,x,y) B. Span(w,z) = Span(y,z) C. Span(x,y,z) = Span(w,y) D...

Homework Statement This is for any vector x in a vector space. The Attempt at a Solution span(x)={x1+x2+...+xn} x1=x2=...=xn x1+x2+...+xn=n*x=a*x a=n therefore ax is equal to span(x) There may be a few holes in my attempt. Sorry I posted this thread in the wrong forum twice.

If we call <a> the "span" of a, then I need some clarification on the concept of span. def. if G is a group and a∈G, then <a> denotes the set of all integral powers of a. Thus, <a> = {a^n : n∈ℤ} thm. Let S be any subset of a group G, and let <S> denote the intersection of all of the...

Let E = span{v1, v2} be the linear subspace of R3 spanned by the vectors v1 = (0,1,-2) and v2 = (1, 1, 1). Find numbers a, b, c so that E = {(x, y, z) of R3 : ax + by + cz = 0} I tried doing this question, but I am totally lost. I know that any vector in E can be represented as a linear...

can explain to me what is mean of span? from book, it say "every vector in the space can be expressed as linear combination of the vectors, then it called the span of vector." but i still can't catch its meaning and concept.

I am having some trouble with this problem... Let W be the set of all vectors of the form: (-5b-4c b c) ^ (that is supposed to be in vector form) Find vectors u and v such that W = Span {u,v}.

Homework Statement This is a general question: What is span in linear algebra? Homework Equations span = linear distribution span(v1, v2, ..., vk) = every linear combination of v1, v2, ..., vk The Attempt at a Solution I've try to visualize what span is, but I just can't "see" it. I don't...

How would i go about telling if vector b (4 row, 1 column) is in the span of the columns of matrix A(4 row, 5 column)? im just not sure what is asking, i know it would be an easy question if i knew what they meant by this.

I would like to know if I have understood the following or not; There are two time dilation equations that I am using; One from special relativity, involving the Lorentz factor; t = \frac{t_0}{\sqrt{1 - v^2/c^2}} And one from general relativity, the Schwarzschild metric; t =...

hey i would greatly appreciate the solutions for the question below 1) determine if p(x) = 9 - 17x + x^2 belong to the span of S {4-x+3x62, 2+5x+x^2}. If it does, express one vector as a linear combination of others. otherwise , justify your answer .

Homework Statement Prove that B={(1,-1,-1),(1,0,1),(0,-1,1)} spans R^3. (Actually, the problem asks to show that B is a basis for R^3. This would require that I prove linear independence AND that it spans R^3. The first is easy, but I'm not sure about the second.) Homework Equations None...

Hey folks - I left my linear book at home for the summer and am having trouble finding this on the Google, so I'm hoping you'll be good for an easy question :) I have a set of vectors that I think spans a vector space, but I've forgotten how to test it. I can make a set of 5 simultaneous...

The Problem: Let S_{1} and S_{2} be subsets of a vector space V. Prove that span\left(S_{1}\cap S_{2}\right)\subseteq span\left(S_{1}\right)\cap span\left(S_{2}\right). Give an example in which span\left(S_{1}\cap S_{2}\right) and span\left(S_{1}\right)\cap span\left(S_{2}\right) are equal and...

Homework Statement (i)Show that the linear span of the vector a1 = (-7, 8, 5) is the line whose equation is x/(-7) = y/8 = z/5 The Attempt at a Solution The problem is, I don't know where or how to start.

If a question asks "does v1, v2, v3 span R4" can i just say no, regardless of what v1 v2 v3 is because v1 v2 and v3 is just 3 dimensions while R4 needs 4 dimensions?

Homework Statement Let S be a subset of a vector space V, and let v be an element of V. Show that span(S) = span(S U {v}) if and only if v is an element of span(S) Homework Equations The Attempt at a Solution I'm honestly not sure how to get started, I've spent time looking...

I have a problem. Suppose that {u1,u1,...,um} are vectors in R^n. Prove, dircetly that span{u1,u2,...,um} is a subspace of R^n. How would I go by doing this?

Alright. As stated in the title above. So, a subspace is a set of vectors that satisfies: 1) It contained the zero vector; 2) It's closed under addition and subtraction. By "closed", it means that when I add another vector in R2 or multiply by a scalar k on A(x)=m, it will end up with...

Homework Statement http://img16.imageshack.us/img16/6606/50381320.jpg Homework Equations Please see above picture The Attempt at a Solution I believe for question a) I just need to add up all the matrices and then row reduce to RREF, which gives me: [1,0,0] [0,1,0] or Do I...

Homework Statement if x_{1}= \begin{pmatrix}2 \\ 1 \\ 3\end{pmatrix} x_{2}= \begin{pmatrix}3 \\ -1 \\ 4\end{pmatrix} x_{3}= \begin{pmatrix}2 \\ 6 \\ 4\end{pmatrix} (i) show that x1,x2 and x3 are linearly dependent (ii) show that x1...

Homework Statement If w is orthogonal to u and v, then show that w is also orthogonal to span ( u , v ) Homework Equations two orthogonal vectors have a dot product equalling zero The Attempt at a Solution I can see this geometrically in my mind, and I know that w . u = 0 and w ...

Homework Statement Suppose V=<Z> where Z is an infinite set, So Z spans V. Suppose that every pair of distinct elements of Z is linearly independent. Is it possible that V is finite dimensional? Justify your answer. Homework Equations The Attempt at a Solution All the vectors...

Hi there! My name is Sander, and I'm a (dutch) Econometrics student at the Rotterdam Erasmus University. This is my first year and I'm getting an introduction to "Matrix Algebra", which is (I think, shoot me if I'm wrong..) quite the same as Linear Algebra (since the book we use is called...

So the question is... Let v1, v2,...,,vn be linearly independent vectors in a vector space V. Show that v2,...,vn cannot span V. I honestly have found myself completely lost lately and I suck at writing proofs. So this is what I see, v1, v2,..., vn is linearly independent iff...

I got a small test tomorrow and i have been working throu exercises but i can't seem to solve this question: Let V be a vector space over a field F, and let S\subset S' be subsets of V. a) Show that span(S) is a subspace of V. b) Show that span(S) is a subset of Span(S'). c) Take...

Homework Statement a)Construct a 3x3 matrix, not in Echelon form, whose columns do NOT span R3. Prove. b)Can a set of 3 vectors Span all of R4? Explain. Homework Equations The Attempt at a Solution a)OK...I can make up plenty of matrices in Echelon form that fit, but how do I...

Not sure if this is "beyond" Calculus but the prereq for the class was Calc II so I thought i'd post here. Homework Statement Could a set of n vectors in Rm span all of Rm? Homework Equations None The Attempt at a Solution Hmm really stuck at this one. I think that it should be...

My professor says that a linearly independent subset of a vector space automatically spans the vector space, and that a subset of a vector space that spans the vector space is automatically linearly independent. I don't understand why either of these is true.

I can read for upto 3 hours before my brain feels saturated. It doesn't matter what it is I am studying after approx. 3 hours in and I can't take in any more. I take a break for 10 minutes but this doesn't seem to help much. When I come back I still feel saturated. How do I expand this? I would...

Homework Statement A radio receiver contains an LC circuit whose natural frequency of oscillation can be adjusted, or tuned, to match the frequency of the incoming radio waves. The adjustment is made by means of a variable capacitor. Suppose that the inductance of the circuit is 11.00 μH. What...

Homework Statement For each s \inR determine whether the vector y is in the subspace of R^4 spanned by the columns of A where y= 6 7 1 s and A = 1 3 2 -1 -1 1 3 8 1 4 9 3 Homework Equations The Attempt at a Solution Can i do this by making an...

Homework Statement Given x_{1}= \begin{pmatrix} 2 \\ 1 \\ 3 \end{pmatrix}, x_{2}= \begin{pmatrix} 3 \\ -1 \\ 4 \end{pmatrix}, x_{3}= \begin{pmatrix} 2 \\ 6 \\ 4 \end{pmatrix} Find the dimension of Span(x_{1}, x_{2}, x_{3}) Homework Equations If V is a vector space...

I can't seem to figure this one out: Question: Let D be a nonempty subset of a vector space V over a field F. Let B be a finite linearly independet subset of span D having n elements. Prove there exists a subset D' of D also having n elements such that span[(D-D') U B] = span(D)...

Homework Statement Let A be the set of all vectors with length 2 and let B be the set of all vectors of length 4. How do you show that the span of the sum of a vector in A and a vector in B is all vectors with lengths between 2 and 4? EDIT: change 4 o 6 I tried drawing triangles but that got...

Hi all, I am having a little trouble understanding the concept of span. I do realize the definition of the span of two vectors is all possible linear combinations of the two vectors but I am trying to make the concept understandable with regards to the problems I have been assigned. Before I...

1. Given b = (-2,3,7), u1= (4,-1,5) and u2= (3,1,3) and u3 = (5,02), determine if vector b is in the span of the remaining vectors Homework Equations 3. You just solve for three equations with three unknowns? -2x + 4y + 3z = 5, 3x - y + z = 0, 7x + 5y + 3z = 2

Homework Statement Show that <S>^{\bot}=S^{\bot} Homework Equations The Attempt at a Solution I manage to show S^{\bot}\subseteq<S>^{\bot}. What about the other way round? Any way of proving without using the concept of basis?

Homework Statement Give a geometric description of the Span {V_{1},V_{2}} for the vectors V_{1} = [8, 2, -6] and V_{2} = [12, 3, -9] Those should be columns but I couldn't figure that out in latex, sorry. 2. The attempt at a solution I have a solution, what I need help with is...

I thought this might be of interest. I hope I haven't missed this being discussed earlier. http://www.photonics.com/content/spectra/2007/April/news/87182.aspx" Doesn't each interaction with a gas molecule cause a different photon to be created? Regards

What do you think the most efficient designs are for a balsa wood span? I was considering an inverted triangle or arch substructure, but I am in the brainstorming process and need other options. In addition, I was considering an extra measure to support the span by buttressing the two cement...

I need some help to understand the concepts of span, basis, and dimension. 1-How do you determine if a set of vectors [in matrix form] span a region? -Do you set the given matrix set to arbitary numbers and see if there is a unique, infinite, or no solution? ie, set a 4X4...

Could a set of n verctors in Rm span all of Rm when n<m? any hits? kinda confused with this span thing.:confused:

Span Proof help please! Hi, I'm working through a textbook on Linear Algebra and just need some info on some proofs. The text gives the Theorem but only provides proof on only one of the parts and I'm really curious as to how to prove b) and also c) so that I can understand the Theorem a...

For each matrix A, find vectors that span the image of A. Give as few vectors as possible. \mathbf{A_1} = \left[ \begin{array}{cc} 1 & 1 \\ 1 & 2 \\ 1 & 3 \\ 1 & 4 \end{array} \right] \mathbf{A_2} = \left[ \begin{array}{cccc} 1 & 1 & 1 & 1 \\ 1 & 2 & 3 & 4 \\ \end{array}...

Heres the problem. A bridge span is 5m high and 20m long. Find the verticle force and the horizontal thrust on each of the piers P in terms of weight suspended from the center of the span. I really hope you can understand the geometry of the problem without the drawing(there was a drawing...

sometimes i think, would the pauli exclusion principle still apply if the fermions span a very large spatial distance? for example if i have a very very loooong chain of condensed electrons, wouldn't it be possible that the electrons at both ends occasionaly occupy the same quantum state?

http://biosingularity.wordpress.com/2005/12/25/scientistists-discover-a-gene-that-regulates-lifespan/ Scientist have discover a gene that regulates ageing and lifespan

Hello everyone, The problem says:Determine which, if, any, of the following sets span R^3? b. {[1 1 -1], [-1 1 1]} note: I'm just transposing them, they should be verical. c. {[1 1 0], [0 1 1], [1 0 0], [1 0 1]} Those are the 2 sets, he showed us how to do them but i got lost on his...