(1) Let S (v1, V2,..., Vn be a set of vectors in a vector space V....

Question

Question

(1) Let S (v1, V2,..., Vn be a set of vectors in a vector space V. (a) Define what does it mean for S to be linearly independ

math algebra

Answer 1

Answer #1

h20 : The ler ie taid to be warly independent 痪 ttti ar auw linear ecuubmarlon o.fl-uue ieqal to Zaro thun livear tomb inah o

Answer 2

Similar Homework Help Questions

Let V be a vector space. Suppose dimV = n and {V1, V2, ..., Vn} is...

Let V be a vector space. Suppose dimV = n and {V1, V2, ..., Vn} is a basis of V. Thei which of the following is always true? a) Any set of n vectors is linearly dependent b) Any linearly dependent set in V is not part of basis c) Any linearly dependent set with n - 1 vectors is a basis d) A linearly independent set with n vectors is a basis
linear independence question 20. Let V1, V2, ...,Vn be linearly independent vectors in a vector space...

linear independence question 20. Let V1, V2, ...,Vn be linearly independent vectors in a vector space V. Show that V2,...,Vn cannot span V.
7. Let T : V → W be a linear transformation, and let v1,v2,...,vn be vectors...

7. Let T : V → W be a linear transformation, and let v1,v2,...,vn be vectors in V. Suppose that T (v1), T (v2), . . . , T (vn) are linearly independent. Show that v1, v2, . . . , vn are linearly independent.

Problem 5: Let V and W be vector spaces and let B = {V1, V2, ...,...

Problem 5: Let V and W be vector spaces and let B = {V1, V2, ..., Un} CV be a basis for V. Let L :V + W be a linear transformation, and let Ker L = {2 € V: L(x)=0}. (a) If Ker L = {0}, show that C = {L(v1), L(02), ..., L(vn) } CW is a linearly independent set in W. (b) If C = {L(01), L(V2),..., L(Un)} C W is a linearly independent set in W,...
Let F be a field and V a vector space over F with the basis {v1, v2, ..., vn}. (a) Consider the s...

Let F be a field and V a vector space over F with the basis {v1, v2, ..., vn}. (a) Consider the set S = {T : V -> F | T is a linear transformation}. Define the operations: (T1 + T2)(v) := T1(v) + T2(v), (aT1)(v) = a(T1(v)) for any v in V, a in F. Prove tat S with these operations is a vector space over F. (b) In S, we have elements fi : V -> F...
(4) Let {V1, V2, ..., Vn} be a basis for a vector space V. If w...

(4) Let {V1, V2, ..., Vn} be a basis for a vector space V. If w is an element of V whose coefficient vector is the zero vector, show that w must be the zero element.

suppose that s=(v1,v2,......vm) is a finite set of linearly independent vectors in V, and w ∈ V some other vector. Let T= S ∪ (W). Prove that T is not linearly independent if and only if w∈ span(s).

suppose that s=(v1,v2,......vm) is a finite set of linearly independent vectors in V, and w ∈ V some other vector. Let T= S ∪ (W). Prove that T is not linearly independent if and only if w∈ span(s).
Prove Lemma a) Fix a basis {v1, v2, . . . , vn} for an n-dimensional...

Prove Lemma a) Fix a basis {v1, v2, . . . , vn} for an n-dimensional vector space V. Define a linear operator T : V → Fn in the following way: For each x = Σni=1 civi ∈ V, define . Then T is a linear operator. b) Let T be a linear operator from V to W. Suppose that {v1, v2, . . . , vn} is a basis for V and {w1, w2, . . . ,...
P4. Prove: If V = {V1, V2, ...,V) is a linearly indepen- dent set of vectors...

P4. Prove: If V = {V1, V2, ...,V) is a linearly indepen- dent set of vectors in R", and if W = {Wx+1, ...,wn} is a basis for the null space of the matrix A that has the vectors V1, V2, ..., Vk as its successive rows, then VUW = {V1, V2, ..., Vk, Wk+1,...,w.} is a basis for R". [Hint: Since V UW contains n vectors, it suffices to show that VUW is linearly independent. As a first step,...

Explain what a basis for a vector space is. How does a basis differ from a span of a vector space...

explain what a basis for a vector space is. How does a basis differ from a span of a vector space? What are some characteristics of a basis? Does a vector space have more than one basis? Be sure to do this: A basis B is a subset of the vector space V. The vectors in B are linearly independent and span V.(Most of you got this.) A spanning set S is a subset of V such that all vectors...