Vector Spaces

Welcome to the Vector Spaces category of Questions LLC! Here, you can dive into the fascinating world of vector spaces and explore a wide range of questions related to this fundamental concept in linear algebra. Whether you are a mathematics enthusiast, a student sharpening your skills, or a professional seeking to deepen your understanding, this category is designed to cater to all levels of expertise. From the basic definitions and properties to more advanced applications, our collection of questions covers everything you need to know about vector spaces. So, get ready to unlock the secrets of vector spaces and expand your knowledge in this captivating area of mathematics!

Questions (54)

Let W be the subspace of R5 spanned by the vectors w1, w2, w3, w4, w5, wherew1 = 2 −1 1 2 0 , w2 = 1 2 0 1 −2 , w3 = 4 3 1 4
1. 4 answers
2. asked by sara
3. 2,386 views
Find a vector r(t) = at^2 + bt + c such that the set B = {2t + 1, t^2 - 1, r(t)} is a basis for P2.Find the values of a, b, c
1. 1 answer
2. asked by Beth
3. 223 views
If U and W are subspaces of a vector space V, show that and are subspaces.
1. 2 answers
2. asked by Ayansa Dabesa soboka
3. 62 views
Let V = {(a, b, c, d) ( (4: b – 2c + d = 0}W = {(a, b, c, d) ( (4: a = d, b = 2c} Find a basis and dimension of a) V b) W c) V
1. 2 answers
2. asked by Ayansa Dabesa soboka
3. 59 views
Find a basis and the dimension of the subspace of generated by{(1, -4, -2, 1), (1, -3, -1, 2), (3, -8, -2, 7)}.
1. 2 answers
2. asked by Ayansa Dabesa soboka
3. 65 views
Find all vectors that are orthogonal to E1 = (1, 0, 0)b) Find all vectors that are orthogonal to both E1 and E3 = (0, 0, 1) c)
1. 2 answers
2. asked anonymously
3. 44 views
Let V be the set of all real-valued continuous functions defined on R1. If f and g are in V, we define f ⊕ g by (f ⊕ g)(t) =
1. 4 answers
2. asked by kirsten
3. 1,856 views
verify The set of all 2 × 2 invertible matrices with the standard matrix addition and scalar multiplication is a vector space
1. 3 answers
2. asked by tasbeer
3. 2,389 views
determine whether the given vector A in M22 belongs to the span (a1,a2,a3) where a1=[1 -1; 0 3]a2=[1 1; 0 2] a3=[2 2; -1 1] and
1. 3 answers
2. asked by sara
3. 854 views
1. Which of the following sets of vectors spans [r^2] ?a) {(1,1), (-2,-2)} b) {(1,1), (1,2)} c) {(1,2), (1/2,2)} d) {(-1,1),
1. 2 answers
2. asked by Jake
3. 539 views
Let V = {(a, b, c, d) ( (4: b – 2c + d = 0}W = {(a, b, c, d) ( (4: a = d, b = 2c} Find a basis and dimension of a) V b) W c)
1. 2 answers
2. asked anonymously
3. 37 views
Do the vectors u = [2 1 -1] v = [1 -1 4] and w [3 2 1] span R3?
1. 2 answers
2. asked by Matthew
3. 204 views
It is given that the vectors v1=[ 1 0]^T and v2 = [ 0 1]^T span the full two-dimensional space R^2(R - set of real numbers)Also
1. 1 answer
2. asked by Ashley
3. 317 views
Consider a set of n vectors in the space R^n.Why do we say that a n*n matrix with those vectors as it's columns, is a basis for
1. 2 answers
2. asked by Ashley
3. 233 views
Is the zero vector space v={0}, linearly independent. If so, why is that?
1. 1 answer
2. asked by Ashley
3. 240 views
Demonstrate that matrixes M(2x2) with the sum of matrixes is a vector space.I am confused. Do i need to demonstrate each
1. 1 answer
2. asked by May
3. 429 views
Find the basis ofM2={(a,b,c,d):a,b,c,d ∈ R}
1. 1 answer
2. asked by Learner
3. 260 views
Find the basis ofM2={(a,b,c,d):a,b,c,d ∈ R}
1. 1 answer
2. asked by Learner
3. 282 views
Let V be the set of ordered pairs [a,b] of realnumbers. Decide with clear reason, whether or not V is a vector space over a
1. 2 answers
2. asked by ...
3. 646 views
Let B be the set of vectors in R^3 given byB = (1, 1, 0) , (1, 1, 1) , (0, 1, −1). 1. For x = (x1, x2, x3)^T a vector in R^3,
1. 1 answer
2. asked by CSCE
3. 375 views
Letv1 = (1, 0, −1) v2 = (0, 2, 2) v3 = (−3, 4, 7) and let W = Span{v1, v2, v3}. What is the dimension of W? Is it 2? Any
1. 1 answer
2. asked by Zabe
3. 331 views
Letv1 = (1, 0, −1) v2 = (0, 2, 2) v3 = (−3, 4, 7) and let W = Span{v1, v2, v3}. Show that W = Span{v1, v2}? How would I go
1. 3 answers
2. asked by Zabe
3. 577 views
Letv1 = (1, 0, −1) v2 = (0, 2, 2) v3 = (−3, 4, 7) and let W = Span{v1, v2, v3}. 1. Show that v3 is a linear combination c1v1
1. 2 answers
2. asked by Zabe
3. 525 views
determine if v1= [ 2 1 0] v2=[ -1 1 3] v3=[ 0 -1 6] spans the vector space of rows with three real entries which has dimension
1. 2 answers
2. asked by kirsten
3. 536 views
how is this not a subspace of R3?The set of all vectors of the form a b c , where a > 0.
1. 1 answer
2. asked by sara
3. 328 views
determine whether or not the given set forms a basis for the indicated subspace:#1 {1,1,0), (1,1,1)} for the subspace of R^3 of
1. 3 answers
2. asked by Anna
3. 531 views
(a) Let S be the set of solutions y(t) to the differential equation dy/dt = -y for t> 0. With addition and scalar multiplication
1. 1 answer
2. asked by Cam
3. 470 views
Let R5[t] be the vector space of all polynomials in t of degree 4 or less with real coefficients. Which of the following subsets
1. 2 answers
2. asked by bdinh
3. 571 views
Prove that If a vector space is of dimension n and a set of vectors spans V, then that set of vectors must be linearly
1. 1 answer
2. asked by John
3. 434 views
How to find the perpendicular to the victor space R^k
1. 1 answer
2. asked by mk
3. 377 views
Let v1= (1,1,2,1)v2= (0,1,3,3) v3= (1,-1,-4,-5) v4= (1,0,-2,-4) a) Let U=span{v1,v2,v3,v4}. Find the dimension of U b) Is span
1. 2 answers
2. asked by Simon
3. 767 views
Find the basis for the following vector space. Please state the dimension of the vector space. S consists of all x in R3 such
1. 3 answers
2. asked by Simon
3. 444 views
Let = the set of all mxn matrices. Is Mmxn a vector space under matrix addition and scalar multiplication?
1. 3 answers
2. asked by Ayansa Dabesa soboka
3. 40 views
Take any vector A in (R^3. Let W be the set of all vectors B in (R^3 where B.A = 0. Discuss whether W is a subspace of (R^3 or
1. 3 answers
2. asked by Ayansa Dabesa soboka
3. 39 views
Find two vectors v and w such that the three vectors u = (1,-1,-1), v and w are linearly independent independent.
1. 1 answer
2. asked by Neeraj
3. 458 views
What is vector space
1. 3 answers
2. asked anonymously
3. 21 views
1/ Prove that the set V=R+ ( the set of all positive real numbers) is a vector space with the following nonstandard operations:
1. 1 answer
2. asked by Tri N
3. 472 views
The vector v lies in the subspace of R^3 and is spanned by the set B = {u1, u2}. Making use of the fact that the set B is
1. 1 answer
2. asked by Kay
3. 400 views
Find a Basis for each of these substances of R^4(a) All vectors whose components are equal (b) All vectors whose component add
1. 2 answers
2. asked by traxx
3. 602 views
V = Mnxn is a space vector formed by all the square matrices.Is W = {A in Mnxn : A^x = A} a subspace of V? Thanks
1. 1 answer
2. asked by Isaac
3. 376 views
hello everyone!i'm breaking my head and desperate how to do it...If i have a vector in linear space V:r v1,v2.....vk,a,b having
1. 1 answer
2. asked by Anatoly Z
3. 312 views
Determine whether {v1, v2, v3} is a basis for R3v1 = [1] [-3] [1] v2 = [-3] [8] [4] v3 = [2] [-2] [2] Put the vectors as rows or
1. 1 answer
2. asked by zinnia
3. 1,113 views
which of the following sets of vectors span R^3?a.){(1, -1, 2), (0, 1, 1)} b.) {1, 2, -1), (6, ,3, 0), (4, -1, 2), (2, -5, 4)}
1. 2 answers
2. asked by chris
3. 1,173 views
Show that a subset W of a vector space V is a subspace of V if and only if the following condition holds: If u and v are any
1. 1 answer
2. asked by chris
3. 363 views
Please can you help me as I have just been introduced to your Help Forum:Determine whether the vectors u, v and w given below
1. 2 answers
2. asked by Charles
3. 845 views
Which of the following subsets of the vector space Mnn are subspaces?(a) The set of all n × n symmetric matrices (b) The set of
1. 2 answers
2. asked by kirsten
3. 1,163 views
let V be the set of all real-valued continuous functions defined on R1. If f and g are in V, we define f ¨’ g by (f ¨’
1. 1 answer
2. asked by sara
3. 711 views
Prove that vectors u, v and w are coplanar if and only if vectors u, v and w are linearly dependent.
1. 2 answers
2. asked by Tess
3. 570 views
If S is the subspace of R^3 containing only the zero vector, what is S perp ? If S is spanned by ( 1 , 1, 1), what is S perp? If
1. 2 answers
2. asked by Frazer
3. 504 views
Determine which of the sets of vectors is linearly independent.A: The set {p1, p2,p3} where p1(t) = 1, p2(t) = t^2, p3(t) = 3 +
1. 1 answer
2. asked by zinnia
3. 479 views

Vector Spaces

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