Span Definition and 209 Threads

Im having trouble under stand the relationships between determinats, span, basis. Given a 3x3 matrix on R3 vector space. * If determinat is 0, it is linearly dependent, will NOT span R3, is NOT a basis of R3. , If determinant is non-zero, its linearly independent, will span R3, is a basis of...

Homework Statement 1. If V is spanned by {v1,v2, ..., vk} and one of these vectors can be written as a linear combination of the other k-1 vectors, prove that the span of these k-1 vectors is also V. Homework Equations A set S = {v1,v2, ..., vk}, k >= 2 is linearly dependent if and only...

Hi everyone! I have the following problem which I don't understand... It is already solved, but there are three questions I have regarding it. The problem says: "Let S be the set of all vectors x=(x_{1}, x_{2}) in \Re^{2} such that x_{1}=1. What is the span of S?" And here is the answer...

Hi I know the dimension is 3, two polynomials has dimension 2 only so it cannot span P2. How would I go about showing it if I were to write it down mathematically? Thanks

Let w=span(w1, w2, ...,wk) where wi are vectors in R^n. Let dot product be inner product for R^n here. Prove that if v*wi=0 for all i-1,2,...,k then v is an element of w^upside down T (w orthogonal).

Homework Statement Homework Equations The Attempt at a Solution It's not so much a homework problem as it is something I was wondering. Our book is horrible, and does not explicitly state that the zero vector is always in the span of two vectors. If I am understanding things right: if v...

Homework Statement Let S be a linearly independent subset of a Hilbert space. Prove that span(S) is a subspace, that is a linear manifold and a closed set, if and only if S is finite. Homework Equations The Attempt at a Solution Assuming S is finite means that S is a closed set...

In order to improve my knowledge of Linear Algebra I am reading Linear Algebra Done Right by Sheldon Axler. In Chapter 2 under the heading Span and Linear Independence we find the following text: "If ( v_1, v_2, ... ... v_m ) is a list off vectors in a vector space V, then each v_j is...

Homework Statement I do understand that in matrix 3x2, the set of vector doesn't span of R3. What should I do to make the set of vector span of R3. Homework Equations The Attempt at a Solution I think adding one more set of vector is the best idea. So, if I can add one more set of...

Homework Statement Show that the two sets of vectors {A=(1,1,0), B=(0,0,1)} and {C=(1,1,1), D=(-1,-1,1)} span the same subspace of R3. Homework Equations {A=(1,1,0), B=(0,0,1)} {C=(1,1,1), D=(-1,-1,1)} The Attempt at a Solution aA+bB=(a,a,0)+(0,0,b)=(a,a,b)...

Homework Statement Find a pair of vectors that span the subspace x+y-2z=0 of R3.Homework Equations x+y-2z=0The Attempt at a Solution I just guessed some numbers since its such a simple equation and came up with (1,-1,0) and (2,0,1). I was just wondering what the standard method is to figure...

I don't wan't a solution I wan't only instructions how to solve this problem: Find a basis for the span: \vec{a_{1}}=(1,\,-1,\,6,\,0),\,\vec{a_{2}}=(3,\,-2,\,1,\,4),\,\vec{a_{3}}=(1,\,-2,\,1,\,-2),\,\vec{a_{4}}=(10,\,1,\,7,\,3)

Homework Statement "In each of the given cases, decide whether the specified elements of the given vector space V (i) are linearly independent, (ii) span V, and (iii) form a basis. Show all reasoning. V is the space of all infinite sequences (a0, a1, a2, ...) of real numbers v1 =...

1. The question goes that "Find two orthogonal vectors that span the same space as the two vectors" The thing is, I know the definition of SPAN, say, a vector b is in span{v1, v2...vp} if x1v1+x2v2+...+xpvp = b. But what's the meaning of "span the same space"? Homework Equations...

show that S and T have the same span in R^3 by showing that the vectors in S are in the span of T and vise versa. S= {(1,0,0), (0,1,0)} T= {(1,2,0), (2,1,0)}im a little confused on how to start off on this problem.. help?!

Hey guys, this question is more or less related to the way Frobenius' theorem is presented in my text. Consider an n - manifold M, an m - dimensional submanifold S of M, and a set of k linearly independent vector fields V^{\mu }_{(a)} such that k \geq m. In order for S to be an integral...

Hello all. This is my first post here. Hope someone can help. Thank you guys in advance. Here is the question: I have a n-by-n matrix A, whose eigenvalues are all real, distinct. And the matrix is positive semi-definite. It has linearly independent eigenvectors V_1...V_n. Now I have known...

For a matrix A, if its nullity is equal to 1, what is the implication of that? What spans its null space? Thanks a lot!

Is there a relationship between the inverse fine-structure constant (alpha) and the life span of elementary particles?

Homework Statement Let U be the span of [ 0 ] [ 2 ] [ 1 ] and [ 0 ] [ 2 ] [ -1] [ 4 ] [ 1 ] Give conditions on a, b, c and d so that [a b c d] (transposed) is in U (as in, give restrictions that are equations of only a, b, c and d. Homework Equations The Attempt at...

Homework Statement find the dimension of the linear span of the given vectors v1 = ( 2, -3, 1) v2 = ( 5, -8, 3) v3 = (-5, 9, -4) Homework Equations The Attempt at a Solution so all i did was make it a matrix and put it in rref and i got [1 0 0] [0 1 0] [0 0 1] does this...

there is an orthonormal group {u1,..,uk} in R^n there is vector v which belongs to R^n prove that if ||v||^2=(v*u1)^2 +..+(v*u_k)^2 then v belongs to the sp{u1..uk} *-is dot product how i tried to solve it: i expanded the orthonormal group {u1,..,uk} to the...

Determine whether the span of the column vectors of the given is in...? Homework Statement determine whether the span of the column vectors of the given matrix is in euclidean space R=4 1 0 1 -1 0 -1 -3 4 1 0 -1 2 -3 0 0 -1 this question is under the inverse of square...

hey i want to find out if the set s = {t2-2t , t3+8 , t3-t2 , t2-4} spans P3 For vectors, i would setup a matrix (v1 v2 v3 v4 .. vn | x) where x is a column vector (x , y ,z .. etc) and reduce the system. If a solution exists then the vectors span the space, if there are no solutions then...

a beam with an effective span of 8.2m is required to carry uniformly disributed loading of gk = 12 kNm-1(in additon to its own self weight) and qk = 10kNm-1. design a suiable reinforced concrete beam using strength class C30 concrete and high yield reinforcement could somone check my...

I have an extremely short attention span and get distracted very easily. I have trouble studying unless there is some background noise. I often study in front of the TV because studying alone quietly is almost torture for me. Also I am quite ashamed of this fact but, I have never finished...

Hey there I was just wondering? Can 2 vectors span R3? let's say I have i and j vectors. What are the examples that show i and j are the basis of R3 and span R3?

Suppose the men in a country have a mean life span of 79 with a standard deviation of 8. And the women in the country have a mean life span of 83 and also a standard deviation of 8. Furthermore, suppose the life spans are normally distributed. What is the mean life span of the entire...

Homework Statement Let A = matrix of size m x n, where m can or cannot be equal to n. The matrix is Rref(A) is in a "perfect staircase" in which exists a unique solution. What can you comment about the Span of the column and row of this matrix? The Attempt at a Solution I am...

Homework Statement Question 1. Let v_{1} = \begin{bmatrix} 1\\ 0\\ -1\\ 0\\ \end{bmatrix},v_{2} = \begin{bmatrix}0\\-1\\0\\1\\\end{bmatrix}, v_{3}=\begin{bmatrix} 1\\ 0\\ 0\\ -1\\ \end{bmatrix} Does {v1, v2, v3} span \mathbb{R}^4 Why or why not? Attempt at Question 1 Span is just a...

Homework Statement Let S be the set of all vectors x = (x1; x2) in R^2 such that x1 = 1: What is the span of S ? Homework Equations ... The Attempt at a Solution x,y from S where x=(1,x2) ,y=(1,y2).Let w be the span of S => (w1,w2)=c1x+c2y...the system looks something like this...

Homework Statement Suppose that S is a countably infinite subset of \ell_2 with the property that the linear span of S′ is dense in \ell_2 whenever S\S′ is finite. Show that there is some S′ whose linear span is dense in \ell_2 and for which S\S′ is infinite. The Attempt at a Solution I...

Here is a brilliant explanation about wealth and human life span in all countries: https://www.youtube.com/watch?v=jbkSRLYSojo&feature=player_embedded

Hi! Homework Statement I can't for the life of me figure out how to do this. I need to find the basis for the span of these four vectors: V1= 3, 1, -2, -4 V2 = -5, -3, 5, 9 V3 = 5, -1, 0, -2 V4 = -1, 5 -6 -8 2. The attempt at a solution I've figured out that the determinant is...

I have the answer, but it makes no sense to me. Can someone explain it? QUESTION: Determine if the vector { [1 3 -1 0]^T, [-2 1 0 0]^T, [0 2 1 -1]^T, [3 6 -3 -2]^T } spans R^4 ANSWER: The vectors span R^4. One way to see this is to observe that the matrix A with these vectors as...

Homework Statement You are given 4 vectors in R^4 which are linearly independent. Do they always span R^4?Homework Equations The Attempt at a Solution Intuitively, I think the answer is yes. I know if I want to show they span R^4, I need to use the general terms, but all I can think of is the...

sir kindly tell me how to know that a matrix of order supose 3*3 is in span of R3 ?...

In dealing with Poisson, Laplace, Schrodinger and other wave equations, one has to deal with propagating and evanescent waves. We know all about the propagating waves - orthogonality and completeness relations, but what about evanescent waves? Do they form a vector space with corresponding...

Homework Statement a wall is inclined to an angle "a" to the horizontal plane. a pendulum of length "l" attached to the wall making an angle "b" with the horizontal (a >b)is let to oscillate. Collision between the bob and the wall is perfectly elastic.show that the time period of the...

Homework Statement Does the vector set span R3? (1,-1,2) and (0,1,1) Homework Equations I'm assuming I set up a matrix... 1 0 a -1 1 b 2 1 c then solve for rref? If my bottom row doesn't contain all zeros, does this mean the vectors do not span r3? The Attempt at a...

Homework Statement The set of vectors u = {1,-2,2,1}, v = {1,3,1,1}, w = {3,4,4,3} cannot span R4. Complete this set to create a set of vectors that will span R4. Show that your set of vectors spans R4. The Attempt at a Solution Let y = {y_1,y_2,y_3,y_4}. I write span{u,v,w,y} as the...

Does a jet engine have a life span?

Memory span as the "quantum" of thought plus golden ratio the basis of everything? I found this paper linked to in wikipedia's article on information theory. After a little bit of background checking, it seems the authors (or at least one of them) is known as being controversial for their...

Homework Statement How to determine if a set of vectors span a space in general? say, V=R^n and you're given a few vectors and asked to determine if they span the space.. how do you do that? Homework Equations The Attempt at a Solution

There is an obvious connecting with the size of a living creature and how long it lives. I know that this is not always true but for the most part it is. I was wondering what this field of research this is called. Is there an average life span to mass ratio?

Show that vectors v1, v2, and v3 span R3. V1=(1,0,0) V2=(2,2,0) V3=(3,3,3) I'm pretty sure I'm doing this wrong? a(V1) +b(V2) +c(V3) = [x,y,z] for (a= 0, b = 0, c = 1/3) [0,0,0] +[0,0,0] +[1,1,1] = [x,y,z] [1,1,1] = [x,y,z]

Can a non square matrix span?

Homework Statement Let V be a vector over a field F. a.) Let x1,...,xn∈V and y1,...,ym∈V. Show that Span(x1,...,xn,y1,...,ym) = Span(x1,...,xn) + Span(y1,...,ym) B.) Let x1, x2, x3, x4 be four linearly independent vectors in V. Show hat Span(x1, x2,x3) ∩ Span(x2, x3, x4) =...

Homework Statement Suppose V is a vector space with operations + and * (under the usual operations) and W = {w1, w2, ... , wn} is a subset of V with n vectors. Show Span{W} is a subspace of V. The attempt at a solution I know that to show a set is a subspace, we need to show...

Homework Statement Suppose the 1.3 km main span of steel for the Golden Gate Bridge had no expansion joints. How much longer would it be for an increase in temperature of 20°C? Homework Equations change in Length=Length*coefficient linear expansion*change in temp. =1300*(11*10^-6/20)*20 The...