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).

Question

Question

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).

math Other-Math

Add a comment Improve this question Transcribed image text

Answer 1

Answer #1

7:46 PM く。 lmplhej 275 276

Add a comment

Answer 2

Similar Homework Help Questions

Suppose V1, V2, V3 is an orthogonal set of vectors in R5. Let w be a vector in span(V1, V2, V3) such that

Suppose V1, V2, V3 is an orthogonal set of vectors in R5. Let w be a vector in span(V1, V2, V3) such that (V1, V1) = 51, (V2, V2) = 638, (V3, V3) = 36, (w, V1) = 153, (w, v2) = 4466, (w, V3) = -36, then W = _______ V1 + _______ V2+ _______ V3.
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.
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.

Please give answer with the details. Thanks a lot! Let T: V-W be a linear transformation between vector spaces V and W...

Please give answer with the details. Thanks a lot! Let T: V-W be a linear transformation between vector spaces V and W (1) Prove that if T is injective (one-to-one) and {vi,.. ., vm) is a linearly independent subset of V the n {T(6),…,T(ền)} is a linearly independent subset of W (2) Prove that if the image of any linearly independent subset of V is linearly independent then Tis injective. (3) Suppose that {b1,... bkbk+1,. . . ,b,) is a...
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,...
(1) Let S (v1, V2,..., Vn be a set of vectors in a vector space V....

(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 independent. (b) Define what does it mean for S to be a spanning set for V. (c) Define what does it mean for S to be a basis for v.

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,...
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...
3. Suppose S = {V1, V2, V3} is a linearly dependent subset of a vector space...

3. Suppose S = {V1, V2, V3} is a linearly dependent subset of a vector space V. Using only the definition of linear dependence and the span of a set, prove that you can remove one vector from S and still have a set with the same span of the original set.

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.

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).

Homework Answers

Add Answer to:
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).

Post as a guest

Earn Coins

Suppose V1, V2, V3 is an orthogonal set of vectors in R5. Let w be a vector in span(V1, V2, V3) such that

7. Let T : V → W be a linear transformation, and let v1,v2,...,vn be vectors...

linear independence question 20. Let V1, V2, ...,Vn be linearly independent vectors in a vector space...

Please give answer with the details. Thanks a lot! Let T: V-W be a linear transformation between vector spaces V and W...

P4. Prove: If V = {V1, V2, ...,V) is a linearly indepen- dent set of vectors...

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

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

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...

3. Suppose S = {V1, V2, V3} is a linearly dependent subset of a vector space...

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

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).

Homework Answers

Add Answer to: 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).

Post as a guest

Earn Coins

Add Answer to:
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).