Let T:V→WT:V→W be an isomorphism. Prove that if {w⃗ 1,w⃗ 2,…,w⃗ n}{w→1,w→2,…,w→n} is a linearly independent...

Question

Question

Let T:V→WT:V→W be an isomorphism. Prove that if {w⃗ 1,w⃗ 2,…,w⃗ n}{w→1,w→2,…,w→n} is a linearly independent...

Let T:V→WT:V→W be an isomorphism. Prove that if {w⃗ 1,w⃗ 2,…,w⃗ n}{w→1,w→2,…,w→n} is a linearly independent set in WW, then the preimages of {w⃗ 1,w⃗ 2,…,w⃗ n}{w→1,w→2,…,w→n} is a linearly independent set in VV.

math algebra

Add a comment Improve this question Transcribed image text

Answer 1

Answer #1

T is Let ai, ai Qll. Given T:VW is an isomorphism. To prove! If {wi, wz was is a linearly independent set in W, then the pre

Add a comment

Answer 2

Similar Homework Help Questions

Let T :V → W be an isomorphism. Prove that if {ū1, ū2, ..., ūn} is...

Let T :V → W be an isomorphism. Prove that if {ū1, ū2, ..., ūn} is a linearly independent set in W, then the preimages of {ū1, ū2, ... , ūn} is a linearly independent set in V.
het T:V W be an isomorphism. Prove That ir & w, wg... ... on} is Set...

het T:V W be an isomorphism. Prove That ir & w, wg... ... on} is Set in wel, then the premages of dwe, log... an} a linearly Independent set knearly Independent 19
het ī: V W be an isomorphism. Prove That ir & w, wg yung is a...

het ī: V W be an isomorphism. Prove That ir & w, wg yung is a is a linearly Set in wl, then the premages of dog. linearly Independent set in v nearly Independent ...., bo} 19

1· Let S {u,v) be a linearly, independent set. Prove that(u+ v.u-v) is linearly independent. 2....

1· Let S {u,v) be a linearly, independent set. Prove that(u+ v.u-v) is linearly independent. 2. Let H :2y1. Prove that H is not a subspace of f2.
1. Determine whether the following set is linearly independent or not. Prove your clas a. [1+1,...

1. Determine whether the following set is linearly independent or not. Prove your clas a. [1+1, 2+2-2,1 +32"} b. {2+1, 3x +3',-6 +2"} 8. Let T be a linear transformation from a vector space V to W over R. . Let .. . be linearly independent vectors of V. Prove that if T is one to one, prove that (un)....(...) are linearly independent. (m) is ) be a spanning set of V. Prove that it is onto, then Tu... h...
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).

7. Let T:V : - W be a linear transformation, and let vi, U2,..., Un be...

7. Let T:V : - W be a linear transformation, and let vi, U2,..., Un be vectors in V. Suppose that T(01), T (v2),..., 1 (un) are linearly independent. Show that 01, V2, ..., Un are linearly independent.
Let {v1, v2,v3} be a linearly independent set in R^n and let v = -αv3 +v1,w...

Let {v1, v2,v3} be a linearly independent set in R^n and let v = -αv3 +v1,w = v2 - αv1, u= v3-αv2 where αER, find all the values of α, where v, w, u are linearly dependent. do not use matrices.
Let W be a subspace of an n-dimensional vector space V over C, and let T:V...

Let W be a subspace of an n-dimensional vector space V over C, and let T:V V be a linear transformation. Prove that W is invariant under T if and only if W is invariant under T- I for any i EC.

Proble m 3. Let T: V ->W be (1) Prove that if T is then T(),... ,T(Fm)} is a linearly indepen dent subset of W (2) P...

Proble m 3. Let T: V ->W be (1) Prove that if T is then T(),... ,T(Fm)} is a linearly indepen dent subset of W (2) Prove that if the image of any linearly in depen dent subset of V is linearly indepen dent then T is injective (3) Suppose that {,... ,b,b^1,...,5} is Prove that T(b1), .. . , T(b,)} is a basis of im(T) (4) Let v1,. Vk} be T(v1),..,T(vk) span W lin ear transform ation between vector...

Let T:V→WT:V→W be an isomorphism. Prove that if {w⃗ 1,w⃗ 2,…,w⃗ n}{w→1,w→2,…,w→n} is a linearly independent...

Homework Answers

Add Answer to:
Let T:V→WT:V→W be an isomorphism. Prove that if {w⃗ 1,w⃗ 2,…,w⃗ n}{w→1,w→2,…,w→n} is a linearly independent...

Post as a guest

Earn Coins

Let T :V → W be an isomorphism. Prove that if {ū1, ū2, ..., ūn} is...

het T:V W be an isomorphism. Prove That ir & w, wg... ... on} is Set...

het ī: V W be an isomorphism. Prove That ir & w, wg yung is a...

1· Let S {u,v) be a linearly, independent set. Prove that(u+ v.u-v) is linearly independent. 2....

1. Determine whether the following set is linearly independent or not. Prove your clas a. [1+1,...

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).

7. Let T:V : - W be a linear transformation, and let vi, U2,..., Un be...

Let {v1, v2,v3} be a linearly independent set in R^n and let v = -αv3 +v1,w...

Let W be a subspace of an n-dimensional vector space V over C, and let T:V...

Proble m 3. Let T: V ->W be (1) Prove that if T is then T(),... ,T(Fm)} is a linearly indepen dent subset of W (2) P...

Let T:V→WT:V→W be an isomorphism. Prove that if {w⃗ 1,w⃗ 2,…,w⃗ n}{w→1,w→2,…,w→n} is a linearly independent...

Homework Answers

Add Answer to: Let T:V→WT:V→W be an isomorphism. Prove that if {w⃗ 1,w⃗ 2,…,w⃗ n}{w→1,w→2,…,w→n} is a linearly independent...

Post as a guest

Earn Coins

Add Answer to:
Let T:V→WT:V→W be an isomorphism. Prove that if {w⃗ 1,w⃗ 2,…,w⃗ n}{w→1,w→2,…,w→n} is a linearly independent...