Question

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.

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

Homework Answers

Answer #1

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
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.
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}
. Let v1,v2,v3,v4 be a basis of V. Show that v1+v2, v2+v3, v3+v4, v4 is a...
. Let v1,v2,v3,v4 be a basis of V. Show that v1+v2, v2+v3, v3+v4, v4 is a basis of V
suppose {V1, V2 , V3 } is a pairwise orthogonal set of nonzero vectors in Rn....
suppose {V1, V2 , V3 } is a pairwise orthogonal set of nonzero vectors in Rn. Show that {V1, V2 , V3 } is also linear independent.
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?
If S is the set of vectors in R^4 (S= {v1, v2, v3, v4, v5}) where,...
If S is the set of vectors in R^4 (S= {v1, v2, v3, v4, v5}) where, v1 = (1,2,-1,1), v2 = (-3,0,-4,3), v3 = (2,1,1,-1), v4 = (-3,3,-9,-6), v5 = (3,9,7,-6) Find a subset of S that is a basis for the span(S).
If S=(v1,v2,v3,v4) is a linearly independent sequence of vectors in Rn then A) n = 4...
If S=(v1,v2,v3,v4) is a linearly independent sequence of vectors in Rn then A) n = 4 B) The matrix ( v1 v2 v3 v4) has a unique pivot column. C) S is a basis for Span(v1,v2,v3,v4)
Determine all real numbers a for which the vectors v1 = (1,−1,1,a,2) v2 = (−1,0,0,1,0) v3...
Determine all real numbers a for which the vectors v1 = (1,−1,1,a,2) v2 = (−1,0,0,1,0) v3 = (1,2,a + 1,1,0) v4 = (2,0,a + 3,2a + 3,4) make a linearly independent set. For which values of a does the set contain at least three linearly independent vectors?
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...
Let S = {v1,v2,v3,v4,v5} where v1= (1,−1,2,4), v2 = (0,3,1,2), v3 = (3,0,7,14), v4 = (1,−1,2,0),...
Let S = {v1,v2,v3,v4,v5} where v1= (1,−1,2,4), v2 = (0,3,1,2), v3 = (3,0,7,14), v4 = (1,−1,2,0), v5 = (2,1,5,6). Find a subset of S that forms a basis for span(S).
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT