Question

Let V be the set of all ordered pairs of real numbers. Consider the following addition...

Let V be the set of all ordered pairs of real numbers. Consider the following addition and scalar multiplication operations V. Let u = (u1, u2) and v = (v1, v2).

• u ⊕ v = (u1 + v1 + 1, u2 + v2 + )

• ku = (ku1 + k − 1, ku2 + k − 1)

Show that V is not a vector space.

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Let V be the set of all ordered pairs of real numbers. Consider the following addition...
Let V be the set of all ordered pairs of real numbers. Consider the following addition and scalar multiplication operations V. Let u = (u1, u2) and v = (v1, v2). • u ⊕ v = (u1 + v1 + 1, u2 + v2 + ) • ku = (ku1 + k − 1, ku2 + k − 1) 1)Show that the zero vector is 0 = (−1, −1). 2)Find the additive inverse −u for u = (u1, u2). Note:...
Consider the set of all ordered pairs of real numbers with standard vector addition but with...
Consider the set of all ordered pairs of real numbers with standard vector addition but with scalar multiplication defined by  k(x,y)=(k^2x,k^2y). I know this violates (alpha + beta)x = alphax + betax, but I'm not for sure how to figure that out? How would I figure out which axioms it violates?
Are the following vector space and why? 1.The set V of all ordered pairs (x, y)...
Are the following vector space and why? 1.The set V of all ordered pairs (x, y) with the addition of R2, but scalar multiplication a(x, y) = (x, y) for all a in R. 2. The set V of all 2 × 2 matrices whose entries sum to 0; operations of M22.
Let V be the set of all triples (r,s,t) of real numbers with the standard vector...
Let V be the set of all triples (r,s,t) of real numbers with the standard vector addition, and with scalar multiplication in V defined by k(r,s,t) = (kr,ks,t). Show that V is not a vector space, by considering an axiom that involves scalar multiplication. If your argument involves showing that a certain axiom does not hold, support your argument by giving an example that involves specific numbers. Your answer must be well-written.
(i) Let u= (u1,u2) and v= (v1,v2). Show that the following is an inner product by...
(i) Let u= (u1,u2) and v= (v1,v2). Show that the following is an inner product by verifying that the inner product hold <u,v>= 4u1v1 + u2v2 +4u2v2 (ii) Let u= (u1, u2, u3) and v= (v1,v2,v3). Show that the following is an inner product by verifying that the inner product hold <u,v> = 2u1v1 + u2v2 + 4u3v3
Consider C as a vector space over R in the natural way. Here vector addition and...
Consider C as a vector space over R in the natural way. Here vector addition and scalar multiplication are the usual addition and multiplication of complex numbers. Show that {1 − i, 1 + i} is linearly independent. Consider C as a vector space over C in the natural way. Here vector addition is the usual addition of complex numbers and the scalar multiplication is the usual multiplication of a real number by a complex number. Show that {1 −...
Exercise 9.1.11 Consider the set of all vectors in R2,(x, y) such that x + y...
Exercise 9.1.11 Consider the set of all vectors in R2,(x, y) such that x + y ≥ 0. Let the vector space operations be the usual ones. Is this a vector space? Is it a subspace of R2? Exercise 9.1.12 Consider the vectors in R2,(x, y) such that xy = 0. Is this a subspace of R2? Is it a vector space? The addition and scalar multiplication are the usual operations.
Let S={(0,1),(1,1),(3,-2)} ⊂ R², where R² is a real vector space with the usual vector addition...
Let S={(0,1),(1,1),(3,-2)} ⊂ R², where R² is a real vector space with the usual vector addition and scalar multiplication. (i) Show that S is a spanning set for R²​​​​​​​ (ii)Determine whether or not S is a linearly independent set
Let R be a relation on set RxR of ordered pairs of real numbers such that...
Let R be a relation on set RxR of ordered pairs of real numbers such that (a,b)R(c,d) if a+d=b+c. Prove that R is an equivalence relation and find equivalence class [(0,b)]R
Let R4 have the inner product <u, v>  =  u1v1 + 2u2v2 + 3u3v3 + 4u4v4...
Let R4 have the inner product <u, v>  =  u1v1 + 2u2v2 + 3u3v3 + 4u4v4 (a) Let w  =  (0, 6, 4, 1). Find ||w||. (b) Let W be the subspace spanned by the vectors u1  =  (0, 0, 2, 1), and   u2  =  (3, 0, −2, 1). Use the Gram-Schmidt process to transform the basis {u1, u2} into an orthonormal basis {v1, v2}. Enter the components of the vector v2 into the answer box below, separated with commas.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT