Question

Give an counter example or explain why those are false a) every linearly independent subset of...

Give an counter example or explain why those are false
a) every linearly independent subset of a vector space V is a basis for V
b) If S is a finite set of vectors of a vector space V and v ⊄span{S}, then S U{v} is linearly independent
c) Given two sets of vectors S1 and S2, if span(S1) =Span(S2), then S1=S2
d) Every linearly dependent set contains the zero vector

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
For each of the following statements, say whether the statement is true or false. (a) If...
For each of the following statements, say whether the statement is true or false. (a) If S⊆T are sets of vectors, then span(S)⊆span(T). (b) If S⊆T are sets of vectors, and S is linearly independent, then so is T. (c) Every set of vectors is a subset of a basis. (d) If S is a linearly independent set of vectors, and u is a vector not in the span of S, then S∪{u} is linearly independent. (e) In a finite-dimensional...
True or False. Explain. Every subset of a linearly independent set is linearly independent.
True or False. Explain. Every subset of a linearly independent set is linearly independent.
4. Prove the Following: a. Prove that if V is a vector space with subspace W...
4. Prove the Following: a. Prove that if V is a vector space with subspace W ⊂ V, and if U ⊂ W is a subspace of the vector space W, then U is also a subspace of V b. Given span of a finite collection of vectors {v1, . . . , vn} ⊂ V as follows: Span(v1, . . . , vn) := {a1v1 + · · · + anvn : ai are scalars in the scalar field}...
Mark the following as true or false, as the case may be. If a statement is...
Mark the following as true or false, as the case may be. If a statement is true, then prove it. If a statement is false, then provide a counter-example. a) A set containing a single vector is linearly independent b) The set of vectors {v, kv} is linearly dependent for every scalar k c) every linearly dependent set contains the zero vector d) The functions f1 and f2 are linearly dependent is there is a real number x, so that...
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...
Answer the following T for True and F for False: __ A vector space must have...
Answer the following T for True and F for False: __ A vector space must have an infinite number of vectors to be a vector space. __ The dimension of a vector space is the number of linearly independent vectors contained in the vector space. __ If a set of vectors is not linearly independent, the set is linearly dependent. __ Adding the zero vector to a set of linearly independent vectors makes them linearly dependent.
Show that the set is linearly dependent by finding a nontrivial linear combination of vectors in...
Show that the set is linearly dependent by finding a nontrivial linear combination of vectors in the set whose sum is the zero vector. (Use s1, s2, and s3, respectively, for the vectors in the set.) S = {(5, 2), (−1, 1), (2, 0)} a) (0, 0) = b) Express the vector s1 in the set as a linear combination of the vectors s2 and s3. s1 =
Complete the proof Let V be a nontrivial vector space which has a spanning set {xi}...
Complete the proof Let V be a nontrivial vector space which has a spanning set {xi} ki=1. Then there is a subset of {xi} ki=1 which is a basis for V. Proof. We will divide the set {xi} ki=1 into two sets, which we will call good and bad. If x1 ≠ 0, then we label x1 as good and if it is zero, we label it as bad. For each i ≥ 2, if xi ∉ span{x1, . ....
Definition. Let S ⊂ V be a subset of a vector space. The span of S,...
Definition. Let S ⊂ V be a subset of a vector space. The span of S, span(S), is the set of all finite linear combinations of vectors in S. In set notation, span(S) = {v ∈ V : there exist v1, . . . , vk ∈ S and a1, . . . , ak ∈ F such that v = a1v1 + . . . + akvk} . Note that this generalizes the notion of the span of a...
Find an example of a nonzero, non-Invertible 2x2 matrix A and a linearly independent set {V,W}...
Find an example of a nonzero, non-Invertible 2x2 matrix A and a linearly independent set {V,W} of two, distinct non-zero vectors in R2 such that {AV,AW} are distinct, nonzero and linearly dependent. verify the matrix A in non-invertible, verify the set {V,W} is linearly independent and verify the set {AV,AW} is linearly dependent
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT