Question

Problem 6.4 What does it mean to say that a set of vectors {v1, v2, ....

Problem 6.4 What does it mean to say that a set of vectors {v1, v2, . . . , vn} is linearly dependent? Given the following vectors show that {v1, v2, v3, v4} is linearly dependent. Is it possible to express v4 as a linear combination of the other vectors? If so, do this. If not, explain why not. What about the vector v3? Anthony, Martin. Linear Algebra: Concepts and Methods (p. 206). Cambridge University Press. Kindle Edition.

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

I had book available with me so was able to answer this question I request you to post complete questions from next time to get your question solved quicker


If you need any further clarification regarding this problem feel free to comment below

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
1. Prove that if {⃗v1, ⃗v2, ⃗v3} is a linear dependent set of vectors in V...
1. Prove that if {⃗v1, ⃗v2, ⃗v3} is a linear dependent set of vectors in V , and if ⃗v4 ∈ V , then {⃗v1, ⃗v2, ⃗v3, ⃗v4} is also a linear dependent set of vectors in V . 2. Prove that if {⃗v1,⃗v2,...,⃗vr} is a linear dependent set of vectors in V, and if⃗ vr + 1 ,⃗vr+2,...,⃗vn ∈V, then {⃗v1,⃗v2,...,⃗vn} is also a linear dependent set of vectors in V.
Let {V1, V2,...,Vn} be a linearly independent set of vectors choosen from vector space V. Define...
Let {V1, V2,...,Vn} be a linearly independent set of vectors choosen from vector space V. Define w1=V1, w2= v1+v2, w3=v1+ v2+v3,..., wn=v1+v2+v3+...+vn. (a) Show that {w1, w2, w3...,wn} is a linearly independent set. (b) Can you include that {w1,w2,...,wn} is a basis for V? Why or why not?
Prove that Let S={v1,v2,v3} be a linearly indepedent set of vectors om a vector space V....
Prove that Let S={v1,v2,v3} be a linearly indepedent set of vectors om a vector space V. Then so are {v1},{v2},{v3},{v1,v2},{v1,v3}，{v2,v3}
If v1 and v2 are linearly independent vectors in vector space V, and u1, u2, and...
If v1 and v2 are linearly independent vectors in vector space V, and u1, u2, and u3 are each a linear combination of them, prove that {u1, u2, u3} is linearly dependent. Do NOT use the theorem which states, " If S = { v 1 , v 2 , . . . , v n } is a basis for a vector space V, then every set containing more than n vectors in V is linearly dependent." Prove without...
Topic: Math - Linear Algebra Focus: Matrices, Linear Independence and Linear Dependence Consider four vectors v1...
Topic: Math - Linear Algebra Focus: Matrices, Linear Independence and Linear Dependence Consider four vectors v1 = [1,1,1,1], v2 = [-1,0,1,2], v3 = [a,1,0,b], and v4 = [3,2,a+b,0], where a and b are parameters. Find all conditions on the values of a and b (if any) for which: 1. The number of linearly independent vectors in this collection is 1. 2. The number of linearly independent vectors in this collection is 2. 3. The number of linearly independent vectors in...
Exercise 6. Consider the following vectors in R3 . v1 = (1, −1, 0) v2 =...
Exercise 6. Consider the following vectors in R3 . v1 = (1, −1, 0) v2 = (3, 2, −1) v3 = (3, 5, −2 )   (a) Verify that the general vector u = (x, y, z) can be written as a linear combination of v1, v2, and v3. (Hint : The coefficients will be expressed as functions of the entries x, y and z of u.) Note : This shows that Span{v1, v2, v3} = R3 . (b) Can R3 be...
Using MATLAB solve: The vectors v1=(1,-1,1), v2=(0,1,2), v3=(3,0,1) span R3. Express w=(x,y,z) as linear combination of...
Using MATLAB solve: The vectors v1=(1,-1,1), v2=(0,1,2), v3=(3,0,1) span R3. Express w=(x,y,z) as linear combination of v1,v2,v3.
Let S={v1,...,Vn} be a linearly dependent set. Use the definition of linear independent / dependent to...
Let S={v1,...,Vn} be a linearly dependent set. Use the definition of linear independent / dependent to show that one vector in S can be expressed as a linear combination of other vectors in S. Please show all work.
Let X be a real vector space. Suppose {⃗v1,⃗v2,⃗v3} ⊂ X is a linearly independent set,...
Let X be a real vector space. Suppose {⃗v1,⃗v2,⃗v3} ⊂ X is a linearly independent set, and suppose {w⃗1,w⃗2,w⃗3} ⊂ X is a linearly dependent set. Define V = span{⃗v1,⃗v2,⃗v3} and W = span{w⃗1,w⃗2,w⃗3}. (a) Is there a linear transformation P : V → W such that P(⃗vi) = w⃗i for i = 1, 2, 3? (b) Is there a linear transformation Q : W → V such that Q(w⃗i) = ⃗vi for i = 1, 2, 3? Hint: the...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT