Question

3. (a) (2 marks) Consider R 3 over R. Show that the vectors (1, 2, 3)...

3. (a) Consider R 3 over R. Show that the vectors (1, 2, 3) and (3, 2, 1) are linearly independent. Explain why they do not form a basis for R 3 .

(b) Consider R 2 over R. Show that the vectors (1, 2), (1, 3) and (1, 4) span R 2 . Explain why they do not form a basis for R 2 .

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
Consider the linearly independent set of vectors B= (-1+2x+3x^2+4x^3+5x^4, 1-2x+3x^2+4x^3+5x^4, 1+2x-3x^2+4x^3+5x^4, 1+2x+3x^2-4x^3+5x^4, 1+2x+3x^3+4x^3-5x^4) in P4(R), does...
Consider the linearly independent set of vectors B= (-1+2x+3x^2+4x^3+5x^4, 1-2x+3x^2+4x^3+5x^4, 1+2x-3x^2+4x^3+5x^4, 1+2x+3x^2-4x^3+5x^4, 1+2x+3x^3+4x^3-5x^4) in P4(R), does B form a basis for P4(R) and why?
Here are some vectors in R 4 : u1 = [1 3 −1 1] u2 =...
Here are some vectors in R 4 : u1 = [1 3 −1 1] u2 = [1 4 −1 1] u3 = [1 0 −1 1] u4 = [2 −1 −2 2] u5 = [1 4 0 1] (a) Explain why these vectors cannot possibly be independent. (b) Form a matrix A whose columns are the ui’s and compute the rref(A). (c) Solve the homogeneous system Ax = 0 in parametric form and then in vector form. (Be sure the...
(a) Consider x^2 + 7x + 15 = f(x) and e^x = g(x) which are vectors...
(a) Consider x^2 + 7x + 15 = f(x) and e^x = g(x) which are vectors of F(R, R) with the usual addition and scalar multiplication. Are these functions linearly independent? (b) Let S be a finite set of linearly independent vectors {u1, u2, · · · , un} over the field Z2. How many vectors are in Span(S)? (c) Is it possible to find three linearly dependent vectors in R^3 such that any two of the three are not...
(a) Do the vectors v1 = 1 2 3 , v2 = √ 3 √ 3...
(a) Do the vectors v1 = 1 2 3 , v2 = √ 3 √ 3 √ 3 , v3=√ 3 √ 5 √ 7, v4 = 1 0 0 form a basis for R 3 ? Why or why not? (b) Let V ⊂ R 4 be the subspace spanned by the vectors a1 and a2, where a1 = (1 0 −1 0) , a2 = 0 1 0 −1. Find a basis for the orthogonal complement V ⊥...
Do the vectors v1 =   1 2 3   , v2 = ...
Do the vectors v1 =   1 2 3   , v2 =   √ 3 √ 3 √ 3   , v3   √ 3 √ 5 √ 7   , v4 =   1 0 0   form a basis for R 3 ? Why or why not? (b) Let V ⊂ R 4 be the subspace spanned by the vectors a1 and a2, where a1 =   ...
Determine if the vectors v1= (3, 0, -3, 6), v2 = ( 0, 2, 3, 1),...
Determine if the vectors v1= (3, 0, -3, 6), v2 = ( 0, 2, 3, 1), and v3 = (0, -2, 2, 0 ) form a linearly dependent set in R 4. Is it a basis of R4 ?
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],...
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 this collection is 3. 4. The number of linearly independent vectors in...
Suppose u, and v are vectors in R m, such that ∥u∥ = 1, ∥v∥ =...
Suppose u, and v are vectors in R m, such that ∥u∥ = 1, ∥v∥ = 4, ∥u + v∥ = 5. Find the inner product 〈u, v〉. (b) Suppose {a1, · · · ak} are orthonormal vectors in R m. Show that {a1, · · · ak} is a linearly independent set
Enlarge the following set to linearly independent vectors to orthonormal bases of R^3 and R^4 {(1,1,1)^t,...
Enlarge the following set to linearly independent vectors to orthonormal bases of R^3 and R^4 {(1,1,1)^t, (1,1,2)^t} could you show me the process, please
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...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT